Question

Work out the size of the angle marked X.
Give your answer correct to 1 decimal place.

Answer 1

The measure of angle x is 41.8 degrees correct to 1 decimal place.

Using the trigonometry ratio to determine the angle of a triangle.

In a right angle triangle where, two sides and one angle is given. We can use the basic trigonometry ratio SOH CAH TOA to determine the angle(s) and the unknown side(s).

Here,

• the hypotenuse is 15cm and
• the opposite side is 10 cm

Using sine function

sin θ = 10/15

θ = sin⁻¹ (2/3)

θ = 41.8°

Answer 2

41.8°

Explanation:

We solve using the Trigonometric function of Sine

Hypotenuse = 15cm

x = θ

Opposite = 10cm

sin θ = Opposite/Hypotenuse

sin θ = 10/15

θ = arc sin ( 10/15)

θ = 41.810314896°

θ = Approximately to 1 decimal place = 41.8°

Therefore, x = θ = 41.8°