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:

$\cos A=\dfrac{b^2+c^2-a^2}{2bc}$

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.

$\cos x=\dfrac{8^2+15^2-11^2}{2(8)(15)}$

$\cos x=\dfrac{64+225-121}{240}$

$\cos x=\dfrac{168}{240}$

$\cos x=0.7$

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°.