Question

Calculate the size of angle x.

Give your answer to 1 decimal place.
8 cm
11 cm
х
15 cm

Answer 1

Given:

Consider the below figure attaches with this question.

To find:

The size of angle x.

Solution:

Law of Cosines:

`\cos A=(b^2+c^2-a^2)/(2bc)`

Three sides of the triangle are 11 cm, 8 cm, 15 cm. Since 11 cm is the opposite side of the angle x, therefore
`a=11`.

Let
`A=x,a=11,b=8,c=15`. Substitute these values in the above formula.

`\cos x=(8^2+15^2-11^2)/(2(8)(15))`

`\cos x=(64+225-121)/(240)`

`\cos x=(168)/(240)`

`\cos x=0.7`

Taking cos inverse on both sides, we get

`x=\cos^(-1) 0.7`

`x=45.572996^\circ`

`x\approx 45.6^\circ`

Therefore, the measure of angle x is 45.6°.