En anglais

Pair the side with its angle

Mathematics · Geometry · ages 15-16

Name ______________________ Date ____________

In triangle PQR, angle P is 30 degrees with opposite side p of 9 cm. Angle R is 90 degrees. Use the sine rule to find side r in cm.
Answer: ______________
What must you pair up before substituting into the sine rule?
- All three angles with each other
- Each side with its opposite angle
- The two longest sides together
Angle A is 30 degrees with opposite side 4 cm, and angle B is 90 degrees. Use the sine rule to find side b, in cm.
Answer: ______________
When is the sine rule the right tool?
- A side and its opposite angle are both known
- Two sides and the included angle are known
- All three sides are known
In triangle ABC, angle A is 30 degrees with opposite side a of 7 cm, and angle C is 45 degrees. Which equation uses the sine rule correctly to find side c?
- c over sin 30 equals 7 over sin 45
- c over sin 45 equals 7 over sin 30
- 7 over sin 45 equals c over sin 30
- c over sin 45 equals 7 over sin 45
Side a is 7 cm opposite angle A of 30 degrees, and side b is 14 cm. Use the sine rule to find angle B, in degrees.
Answer: ______________
Angle A is 30 degrees with opposite side 6 cm, and angle B is 90 degrees. Find side b, in cm, using the sine rule.
Answer: ______________
In triangle ABC, angle A is 30 degrees with opposite side a of 5 cm, and side b is 6 cm. Use the sine rule to find the obtuse value of angle B, in degrees. Round your answer to 1 decimal place.
Answer: ______________
You know two sides and the angle trapped between them, but no opposite pair. Which rule fits?
- The sine rule
- The cosine rule
- Pythagoras, whatever the angle
In triangle ABC, angle A is 30 degrees, side a is 4 cm, and side b is 7 cm. When finding angle B, which values are candidates?
- Only the calculator value, since calculators never lie
- Only 180 minus the calculator value
- Both the calculator value and 180 minus it
- Neither, the answer is unique

Answer key

For grown-ups. Fold this page away before handing over the rest.

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18 · Pair p with P and r with R, then r equals 9 over sin 30, which is 9 over 0.5, so 18.
Each side with its opposite angle · The rule links each side to the sine of its opposite angle.
8 · b equals 4 times sin 90 over sin 30, which is 4 over 0.5.
A side and its opposite angle are both known · One full side-angle pair starts the rule; without it you switch tools.
c over sin 45 equals 7 over sin 30 · Side c pairs with angle C and side 7 pairs with angle A, so c over sin 45 equals 7 over sin 30.
90 · Sin B equals 14 times 0.5 over 7, which is 1, so B is 90 degrees.
12 · b equals 6 over sin 30, which is 6 over 0.5.
143.1 · Sin B equals 6 times 0.5 over 5, which is 0.6. The acute value is about 36.9 degrees, so the obtuse partner is about 143.1 degrees, and it leaves a positive third angle.
The cosine rule · With no full pair the sine rule cannot start, so the cosine rule takes over.
Both the calculator value and 180 minus it · Sin B equals 0.875, giving an acute value near 61 degrees and an obtuse partner near 119 degrees. Both leave a positive third angle, so both are candidates.