Chapter

Chapter 8
Section

Chapter Review on Trigonometry of Acute Triangles

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Solutions
15 Videos

Find the length of `x`

. to the nearest centimetre.

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Q1

Find the measure of `\angle P`

, to the nearest degree.

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Q2

Solve each triangle. Round answers to the nearest unit, if necessary.

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Q3a

In acute `\triangle NRC`

, `\angle N = 47^o`

, `\angle R =`

80°, and `r= 27mm`

.

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Q3b

Three billiard balls are lying as shown.

The white cue ball is 55 cm from the red ball and 62 cm from the black ball. The line segment from the red ball to the white ball and the line segment from the red ball to the black ball form an angle of 82°.

a) How far apart are the red and black balls, to the nearest centimetre?

b) Find the measures of the other angles in the triangle formed by these three billiard balls, to the nearest degree.

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Q4

Find the length of t, to the nearest metre.

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Q5

Solve the triangle. Round answers to the nearest unit, if necessary.

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Q6a

In acute `\triangle EQW`

, `AW =`

77°, `e = 11 km`

, and `q = 14km`

.

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Q6b

Lucy’s space shuttle is 35 km from her mother ship and 42 km from a space station. From Lucy’s point of View, the mother ship and space station appear to be 49° apart, as shown.

a) How far apart are the mother ship and the space station, to the nearest kilometre?

b) From the space station, by what angle do the shuttle and mother ship appear to be separated, to the nearest degree?

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Q7

Find `\angle B`

.

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Q8

Solve the triangle. Round answers to the nearest tenth of a degree.

In acute `\triangle VSF`

, `v = 2.9 km, s =3.5 km`

, and `f = 3.0 km`

.

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Q9a

Solve the triangle. Round answers to the nearest tenth of a degree.

In acute `\triangle SBZ`

, `s = 19 m, b =21 m`

, and `z = 13 m`

.

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Q9b

While flying, a helicopter pilot spots a water tower that is 4.8 km away to the north. At the same time, she also sees a monument that is 5.6 km away to the south. The tower and the monument are separated by a distance of 7.0 km along the flat ground. Find the angles at which the pilot is viewing the water tower and the monument, to the nearest degree.

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Q10

A person on the ground is directly between two helicopters that are flying toward each other at the same altitude. The first helicopter is 2.0 km away from the observer, at an angle of elevation of 30°, while the second helicopter is 3.5 km away. Round answers to the nearest tenth of a kilometre, if necessary.

a) Draw a diagram and label the known information.

b) How far apart are the helicopters?

c) What is their altitude?

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Q11

Putin's Rock is located on the shore of the Grape Peninsula. The measurements shown were taken at low tide.

Find the height of Putin's Rock, to the nearest metre.

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Q12