Here showcasing some of the trigonometry math problems

## Trigonometry math problem 1

A man 30 meters away from a tree and looking at the top of the tree at an angle of 30 degrees then find the height of the tree (Height of the man is 1.5 meters)

## Solution to problem 1

We can picture this math problem like this

Here OA = 1.5 meters is the height of the man and XY is the height of the tree, We need to find the value of XY to solve this math problem

AB is parallel to the ground then ∠BAY = 30° (Man looking at 30 degrees) and AB = 30 meters (distance from the tree)

From triangle BAY, Let BY = x then

tan ∠BAY = BY/AB

⇒ tan 30° = x/30

⇒ 1/√3 = x/30

so, x = 10√3 meters

⇒ XY = 10√3 +BX = 10√3 + 1.5

**Height of the tree = 10√3 + 1.5 = meters**

## Trigonometry math problems to find the side of the triangle

## Trigonometry math problem 2

ABC is a triangle with sides 4 cm & 5 cm and ∠ABC = 60°, then find the radius of the circumcircle

## Solution to problem 2

Apply cosine rule in triangle ABC

BC^{2} = AB^{2} + AC^{2} – 2 *×* AB *×* AC *×* cos A

⇒ BC^{2} = 5^{2} + 4^{2} – 2 *×* 5 *×* 4 *×* cos 60*°*

⇒ BC^{2} = 25 + 16 – 2 *×* 5 *×* 4 *×* 1/2 = 41 – 20

so, BC^{2 }= 21

⇒ BC = *√*21 cm

Apply sine rule in triangle ABC then

D ( Diameter) = BC/sin A

⇒ D = *√*21/sin 60 = *√*21/(*√*3/2)

⇒ D = 2*√*7 cm

then, **Radius of the circumcircle = √7 cm**

## Trigonometry math problem 3

If sin A = *√*3/2 then find the value of cos A

## Solution to problem 3

We can solve this problem with help of sin^{2} A + cos^{2} A = 1 identity

sin^{2} A + cos^{2} A = 1

⇒ (√3/2)^{2} + cos^{2} A = 1

⇒ 3/4 + cos^{2} A = 1

so, cos^{2} A = 1 – 3/4

⇒ cos^{2} A = 1/4

then, **cos A = 1/2**

## Trigonometry math problem 4

ABC is a triangle with sides 4 cm & 6 cm and ∠ABC = 30°, then find the area of the triangle

## Solution to problem 4

Area of the triangle = ½ × AB × AC × sin A

⇒ Area of the triangle = ½ × 6 × 4 × sin 30°

⇒ Area of the triangle = ½ × 6 × 4 × ½

so, the area of the triangle = 6 cm^{2}