Trigonometric Ratios (Ex 6A)

Year 10 Mathematics Core · Cambridge Ch 6, §6A · Mr Wong

Name

Class

Date

Learning intentions.

Label the hypotenuse, opposite and adjacent sides of a right triangle relative to a given angle
Choose the correct trig ratio (sin, cos or tan) for the information you have
Solve for an unknown side length when the unknown is in the numerator or the denominator

Key results — SOHCAHTOA

$\sin\theta=\dfrac{O}{H}\qquad \cos\theta=\dfrac{A}{H}\qquad \tan\theta=\dfrac{O}{A}$

$O$ = opposite · $A$ = adjacent · $H$ = hypotenuse (opposite the right angle)

Warm-up — calculator and ratio choice

1. Use a calculator (degree mode), correct to 3 d.p.

a $\cos 37^\circ=$

b $\sin 72^\circ=$

c $\tan 50^\circ=$

d $\cos 21.4^\circ=$

2. For each triangle, state which ratio (sin / cos / tan) you would use to find $x$. Do not solve.

a) ratio = ______

b) ratio = ______

c) ratio = ______

Part A — Unknown is the numerator

For each, set up the trig equation and solve for $x$ to 2 d.p.

3. Solve the following.

a $\sin 35^\circ=\dfrac{x}{12}$ $x=$

b $\cos 42^\circ=\dfrac{x}{9}$ $x=$

c $\tan 28^\circ=\dfrac{x}{5}$ $x=$

d $\cos 61^\circ=\dfrac{x}{8.4}$ $x=$

e $\sin 70^\circ=\dfrac{x}{15}$ $x=$

f $\tan 54^\circ=\dfrac{x}{4.6}$ $x=$

Trig 6A — continued

Part B (unknown in the denominator) · Application

Name

Part B — Unknown is the denominator

Cross-multiply first, then divide. Answers to 2 d.p.

4. Solve the following.

a $\sin 40^\circ=\dfrac{14}{x}$ $x=$

b $\cos 38^\circ=\dfrac{25}{x}$ $x=$

c $\tan 52^\circ=\dfrac{9}{x}$ $x=$

d $\sin 72^\circ=\dfrac{30}{x}$ $x=$

e $\cos 45^\circ=\dfrac{18}{x}$ $x=$

f $\tan 67^\circ=\dfrac{12.5}{x}$ $x=$

Part C — Triangles (draw the equation from the picture)

5. Find $x$ in each. Set up the trig equation first, then solve to 2 d.p.

(a) find $x$

(b) find $x$

Challenge — apply the ratio

6. A right triangle has a $40^\circ$ angle, with the side opposite that angle measuring $7$ cm. (a) Find the length of the hypotenuse to 2 d.p. (b) Find the length of the third side (adjacent) to 2 d.p.

7. A ladder of length $4.5$ m leans against a wall and makes an angle of $72^\circ$ with the ground. How far up the wall does the top of the ladder reach? Answer to 2 d.p.