Solutions — Trig 6A Worksheet
Year 10 Mathematics Core · Cambridge Ch 6, §6A · Mr Wong
ANSWER KEY
Warm-up
Q1. Calculator values (3 d.p.):
a $0.799$
b $0.951$
c $1.192$
d $0.931$
Q2. Which ratio (based on what is known):
a $\cos$ (hyp 7 and adj $x$)
b $\tan$ (adj 2 and opp $x$)
c $\sin$ (hyp 10.3 and opp $x$)
Part A — Unknown in the numerator
Q3. Solve $x = \text{(side)} \times \text{(ratio)}$ to 2 d.p.
a $x\approx 6.88$ ($12\sin 35^\circ$)
b $x\approx 6.69$ ($9\cos 42^\circ$)
c $x\approx 2.66$ ($5\tan 28^\circ$)
d $x\approx 4.07$ ($8.4\cos 61^\circ$)
e $x\approx 14.10$ ($15\sin 70^\circ$)
f $x\approx 6.33$ ($4.6\tan 54^\circ$)
Part B — Unknown in the denominator
Q4. Solve $x = \text{(side)} \div \text{(ratio)}$ to 2 d.p.
a $x\approx 21.78$ ($14/\sin 40^\circ$)
b $x\approx 31.73$ ($25/\cos 38^\circ$)
c $x\approx 7.03$ ($9/\tan 52^\circ$)
d $x\approx 31.54$ ($30/\sin 72^\circ$)
e $x\approx 25.46$ ($18/\cos 45^\circ$)
f $x\approx 5.31$ ($12.5/\tan 67^\circ$)
Part C — From the diagrams
Q5. Set up and solve.
a
$\cos 27^\circ=\dfrac{x}{11}\;\Rightarrow\;x=11\cos 27^\circ\approx$ $9.80$ cm
b
$\tan 69^\circ=\dfrac{x}{38}\;\Rightarrow\;x=38\tan 69^\circ\approx$ $98.99$ mm
c
$\sin 33^\circ=\dfrac{21}{x}\;\Rightarrow\;x=\dfrac{21}{\sin 33^\circ}\approx$ $38.56$ m
Challenge
Q6. Right triangle, $40^\circ$ angle, opposite side $7$ cm:
a
$\sin 40^\circ=\dfrac{7}{h}\;\Rightarrow\;h=\dfrac{7}{\sin 40^\circ}\approx$ $10.89$ cm (hypotenuse)
b
$\tan 40^\circ=\dfrac{7}{a}\;\Rightarrow\;a=\dfrac{7}{\tan 40^\circ}\approx$ $8.34$ cm (adjacent)
Q7. Ladder 4.5 m, angle $72^\circ$ with ground, height = opp side:
·
$\sin 72^\circ=\dfrac{h}{4.5}\;\Rightarrow\;h=4.5\sin 72^\circ\approx$ $4.28$ m up the wall