Question

Solve for the missing angle measures:

ے خرم
D
x
x
5
15
9
E
y
B
x
E
24
y
18
R
y
x
S
12
N

Answer 1

All the angles using trigonometric ratio are:

1) x = 32°

y = 58°

2) x = 16.26°

y = 73.74°

3) x = 53.13°

y = 36.87°

4) x = 56.31°

y = 33.69°

How to use trigonometric ratios?

There are three main trigonometric ratios which are:

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

1) Using tangent trigonometric ratio gives us:

tan x = 5/8

x = tan⁻¹(5/8)

x = 32°

tan y = 8/5

y = tan⁻¹(8/5)

y = 58°

2) Using tangent trigonometric ratio gives us:

tan x = 7/24

x = tan⁻¹(7/24)

x = 16.26°

tan y = 24/7

y = tan⁻¹(24/7)

y = 73.74°

3) Using cosine trigonometric ratio gives us:

cos x = 9/15

x = cos⁻¹(9/15)

x = 53.13°

Using sin trigonometric ratio gives us:

sin y = sin⁻¹(9/15)

y = 36.87°

4) Using tangent trigonometric ratio gives us:

tan x = 18/12

x = tan⁻¹(18/12)

x = 56.31°

tan y = 12/18

y = tan⁻¹(12/18)

y = 33.69°