Question

A = 14.9 cm, b = 14.1 cm and C = 5.7 cm for the triangle shown below.

X
a
-- C
b-
Work out the value of x rounded to 1 DP.
The diagram is not drawn to scale.

Answer 1

X is 22.5°

Explanation:

» Let's assume our diagram is as above, from trigonometric ratio:

`{ \tt{ \red{ \sin( \theta) = (opposite)/(hypotenuse) }}} \\`

• theta is X
• opposite is a
• hypotenuse is c

`{ \tt{ \sin(x) = (a)/(c) }} \\ \\ { \tt{ \sin(x) = (5.7)/(14.9) }} \\ \\ { \tt{ \sin(x) = 0.3826}} \\ \\ { \tt{x = { \sin }^( - 1)(0.3826) }} \\ \\ { \boxed{ \tt{x = 22.5 \degree}}}`