Calculating an angle

The three trigonometric ratios can be used to calculate the size of an angle in a right-angled triangle.

Example

Calculate the angle QPR. Give the answer to one decimal place.

Triangle (PQR) with unknown angle x

Label the sides of the triangle o, a and h.

Next choose the correct ratio from s^o_h~c^a_h~t^o_a.

In the triangle the lengths o and a are known.

Use: \tan{x} = \frac{o}{a}

\tan{x} = \frac{5}{7}

\tan{x} = 0.714285 \dotsc. Do not round this answer yet.

To calculate the angle use the inverse tan button on the calculator ( \tan^{-1}).

x = 35.5^\circ

Question

Calculate the angle KJL. Give the answer to one decimal place.

Triangle (JKL) with unknown angle x

Label the sides of the triangle o, a and h.

Next choose the correct ratio from s^o_h~c^a_h~t^o_a.

In the triangle the lengths a and h are known.

Use: \cos{x} = \frac{a}{h}

\cos{x} = \frac{4}{6}

\cos{x} = 0. \dot{6}. Do not round this answer yet.

To calculate the angle use the inverse cos button on the calculator ( \cos^{-1}).

x = 48.2^\circ