trigonometry | Jamb Mathematics
paragraph
Get ready to conquer trigonometry in grand style! This exam will test your understanding of angles, identities, and
real-world applications, so sharpen your skills and bring your A-game. Dive into your formulas, practice those
tricky problems, and prepare to excel with confidence!
paragraph
Are you preparing for your JAMB Mathematics exam and feeling a bit uncertain about how to approach the topic
of trigonometry? Don’t worry—you’re in the right place! This lesson is here to break it down in a simple,
clear, and engaging way, helping you build the strong foundation you need to succeed. Whether you're
struggling with complex questions or just seeking a quick refresher, this guide will boost your understanding
and confidence. Let’s tackle trigonometry together and move one step closer to achieving your exam success!
Blissful learning.
paragraph
calculation problem involving trigonometrical ratios of angles;
paragraph
Question 1:
Find the value of .
olution:
Using standard trigonometric values,
.
.
Question 2:
Find the value of .
Solution:
Using standard trigonometric values,
.
.
Question 3:
If , find .
Solution:
Using the Pythagorean identity:
.
.
Question 4:
Evaluate .
Solution:
Using standard values,
.
.
Question 5:
Find .
Solution:
.
Question 6:
Find .
Solution:
.
Question 7:
Find .
Solution:
.
Question 8:
Evaluate .
Solution:
Using the identity ,
.
.
Question 9:
Solve for : , where .
Solution:
occurs at
.
.
Question 10:
Find .
Solution:
.
Question 11:
Find .
Solution:
.
Question 12:
Evaluate .
Solution:
.
Question 13:
Find .
Solution:
.
Question 14:
Evaluate .
Solution:
, which is undefined.
Question 15:
Find .
Solution:
.
Question 16:
Solve , for .
Solution:
occurs at
.
.
Question 17:
Find .
Solution:
.
Question 18:
Evaluate .
Solution:
.
Question 19:
Find .
Solution:
.
Question 20:
Find .
Solution:
.
paragraph
Calculation problems on applying special angles to solve problems in trigonometry
paragraph
Question 1:
Evaluate .
Solution:
Using known values,
and
.
and
.
Question 2:
Find if and .
Solution:
From known values,
at .
Since , the valid solution is .
at .
Since , the valid solution is .
Question 3:
Find .
Solution:
Using the Pythagorean identity:
.
.
Question 4:
Find .
Solution:
.
Question 5:
Find .
Solution:
.
Question 6:
Evaluate .
Solution:
.
Question 7:
Find .
Solution:
Using known values:
.
.
Question 8:
Find .
Solution:
.
Question 9:
Solve for if and .
Solution:
at .
Question 10:
Find .
Solution:
.
Question 11:
Evaluate .
Solution:
.
Question 12:
Find .
Solution:
.
Question 13:
Find .
Solution:
.
Question 14:
Solve for .
Solution:
.
Question 15:
Find .
Solution:
.
paragraph
Calculation problems involving angles of elevation and depression
paragraph
Question 1:
A person standing 50 m away from a building observes the top at an angle of elevation of . Find the height of the building.
Solution:
Using the tangent formula:
m.
m.
Question 2:
A ladder leans against a wall, making a angle with the ground. If the foot of the ladder is 4 m from the wall, find the length of the ladder.
Solution:
Using the cosine rule:
m.
m.
Question 3:
A kite is flying at a height of 30 m. The string makes an angle of with the ground. Find the length of the string.
Solution:
Using the sine rule:
m.
m.
Question 4:
A person at a distance of 20 m from a lamppost observes the top at an elevation of . Find the height of the lamppost.
Solution:
Using the tangent formula:
m.
m.
Question 5:
A ship is spotted at sea from a lighthouse at a height of 50 m. The angle of depression is . Find the distance of the ship from the base of the lighthouse.
Solution:
Using the tangent formula:
m.
m.
Question 6:
A plane is flying at a height of 1000 m. The angle of depression to a point on the ground is . Find the horizontal distance of the plane from the point.
Solution:
Using the tangent formula:
m.
m.
Question 7:
A 6 m tree casts a shadow of 4 m. Find the angle of elevation of the sun.
Solution:
Using the tangent formula:
.
.
Question 8:
A drone flies at a height of 120 m above the ground. The angle of depression to an observer is . Find the horizontal distance between the observer and the drone.
Solution:
Using the tangent formula:
m.
m.
Question 9:
A balloon rises to a height of 150 m. The angle of elevation from a point 200 m away is . Find .
Solution:
Using the tangent formula:
.
.
Question 10:
An observer is 30 m from a tower and sees the top at . Find the tower's height.
Solution:
Using the tangent formula:
m.
m.
Question 11:
A person at a height of 50 m observes a boat at an angle of depression of . Find the boat's distance from the observer.
Solution:
Using the sine rule:
m.
m.
Question 12:
A bridge is built over a river. The angle of depression from the bridge to a boat is . If the bridge is 70 m above water, find the boat's distance from the bridge base.
Solution:
Using the tangent formula:
m.
m.
Question 13:
A ramp is inclined at and has a length of 10 m. Find the height it reaches.
Solution:
Using the sine rule:
m.
m.
Question 14:
A 15 m ladder leans against a wall, making a angle with the ground. Find the height it reaches on the wall.
Solution:
Using the sine rule:
m.
m.
Question 15:
An observer 50 m away sees the top of a tree at . Find the tree's height.
Solution:
Using the tangent formula:
m.
m.
paragraph
Calculation problems involving area and solution of triangles
paragraph
Question 1:
Find the area of a triangle with base m and height m.
Solution:
Using the area formula:
m².
m².
Question 2:
Find the area of a triangle with sides m, m, and included angle .
Solution:
Using the formula:
m².
m².
Question 3:
A triangle has sides m, m, and m. Find its area using Heron's formula.
Solution:
First, find the semi-perimeter:
Using Heron's formula:
m².
m².
Question 4:
Solve for angle in a triangle where , .
Solution:
Using the sum of angles in a triangle:
.
.
Question 5:
Find the third side of a triangle where , , and included angle .
Solution:
Using the Pythagorean theorem:
.
.
Question 6:
Find the missing side in a triangle where , , and using the Law of Sines.
Solution:
Using the Law of Sines:
First, find :
First, find :
Now, solving for :
.
.
Question 7:
Find the area of an equilateral triangle with side length m.
Solution:
Using the formula for the area of an equilateral triangle:
m².
m².
Question 8:
In a right-angled triangle, the hypotenuse is m, and one of the angles is . Find the opposite side.
Solution:
Using the sine function:
m.
m.
Question 9:
A triangle has sides m, m, and m. Find the largest angle.
Solution:
Using the Law of Cosines:
.
.
Question 10:
Find the area of a triangle with sides m, m, and m.
Solution:
First, find the semi-perimeter:
Using Heron's formula:
m².
m².
paragraph
Calculation problems involving Bearings
paragraph
Question 1:
A ship sails 10 km due east and then 24 km due north. Find the bearing of its final position from its starting point.
Solution:
-
The ship moves 10 km east and 24 km north, forming a right-angled triangle.
-
The bearing is measured clockwise from the north.
-
Using the tangent function:
-
The bearing is:.
Question 2:
A plane flies from point A on a bearing of for 50 km, then turns and flies 60 km due east. Find the bearing of its final position from A.
Solution:
-
The first leg is at , meaning it moves southeast.
-
The second leg is due east.
-
Using vector addition and trigonometry, find the total displacement and use inverse tangent to determine the final bearing.
-
Calculate resultant distance and bearing using:.
-
Solve for and adjust to get the correct bearing.
Question 3:
A car moves 30 km on a bearing of and then 40 km on a bearing of . Find its resultant displacement and bearing from the starting point.
Solution:
- Resolve the movements into horizontal and vertical components.
- Use the cosine and sine functions to determine total displacement.
- Use inverse tangent to find the resultant angle and adjust it to standard bearings.
Question 4:
An aircraft flies 100 km on a bearing of and then 80 km on a bearing of . Find its final position relative to the starting point.
Solution:
- Break both legs into x- and y-components using trigonometry.
- Sum the components and use the Pythagorean theorem to find the final distance.
- Use inverse tangent to determine the bearing.
Question 5:
A person walks 5 km on a bearing of and then 12 km due north. Find the resultant displacement and bearing.
Solution:
- Resolve movements into x- and y-components.
- Compute resultant displacement using Pythagoras' theorem.
- Find the angle using inverse tangent and adjust for correct bearing.
Question 6:
A ship sails 15 km due north, then 20 km due east. Find the bearing of its final position from the starting point.
Solution:
-
The ship moves in a right-angled triangle.
-
Use:..
-
The final bearing is:.
Question 7:
An observer sees a lighthouse at a bearing of . After moving 5 km north, the new bearing is . Find the distance to the lighthouse.
Solution:
- Use trigonometry and the Law of Sines to determine the distance to the lighthouse.
Question 8:
A plane flies 80 km on a bearing of , then 60 km on a bearing of . Find its final displacement and bearing from the starting point.
Solution:
- Resolve movements into x- and y-components.
- Compute the resultant displacement.
- Use inverse tangent to determine the bearing.
Question 9:
A ship sails 40 km on a bearing of , then 30 km on a bearing of . Find its final position.
Solution:
- Resolve each leg into components.
- Find the total displacement using the Pythagorean theorem.
- Use inverse tangent for the bearing.
Question 10:
A hiker moves 8 km on a bearing of , then 6 km on a bearing of . Find the resultant displacement and final bearing.
Solution:
- Decompose the movements into components.
- Sum the x- and y-components.
- Use the Pythagorean theorem and inverse tangent to get the final displacement and bearing.
paragraph
Thank you for taking the time to read my blog post! Your interest and engagement mean so much to me, and I hope
the content provided valuable insights and sparked your curiosity. Your journey as a student is inspiring, and
it’s my goal to contribute to your growth and success.
paragraph
If you found the post helpful, feel free to share it with
others who might benefit. I’d also love to hear your thoughts, feedback, or questions—your input makes this
space even better. Keep striving, learning, and achieving! 😊📚✨
paragraph
I recommend you check my Post on the following:
paragraph
- Jamb Mathematics- Lesson notes on trigonometry for utme Success
paragraph
This is all we can take on "Jamb Mathematics - Lesson Notes on trigonometry for UTME Candidate"
paragraph