Chapter

Chapter 8
Section

Practice Test on Trigonometry of Acute Triangles

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Solutions
15 Videos

Find `b`

.

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Q1

Find `r`

.

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Q2

Find the measure of the indicated angle, to the nearest degree.

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Q3

Find the measure of the indicated angle, to the nearest degree.

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Q4

Two wires are supporting a tent pole, as shown.

a) How far apart are the wires fixed in the ground, to the nearest tenth of a metre?

b) Find the angle each wire makes with the ground, to the nearest degree. State any assumptions you make.

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Q5

Cheryl is trying to hit her golf ball between two trees. She estimates the distances shown. Within what angle must Cheryl make her shot, in order to pass between the trees? Round to the nearest tenth of a degree.

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Q6

Solve `\triangle XYZ`

. Round the side length to the nearest tenth of a metre and the angle measures to the nearest degree.

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Q7

In acute `\triangle NTW`

, `LN =`

54°, `n = 2.3 km`

, and `w = 1.8 km`

.

a) Sketch this triangle and label the given information.

b) Solve this triangle. Round the side length to the nearest tenth of a metre and the angle measures to the nearest degree.

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Q8

Students of Fowler’s Aeronautical School have this crest on their pilot’s cap. Find the total length of gold trim needed to make a crest, to the nearest tenth of a centimetre. State any assumptions you make.

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Q9

Use the measurements given to find the height of the Peace Tower in Ottawa, to the nearest metre.

`AB = 50 m`

, `\angle XAY = 43^o`

, `\angle XAB = 60^o`

, `\angle ABX = 82^o`

.

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Q10

Tess was flying from Toronto to Hamilton at night. She noticed that her heading indicator was malfunctioning and decided to check her position.

She called Hamilton Tower and St. Catharines Radio. knowing that the stations were 50 km apart.

Hamilton reported that the position of her plane formed an angle of `65^o`

with the line joining the two stations. St. Catharines reported that her position made an angle of `48^o `

.

How far was the plane from Hamilton. to the nearest kilometre?

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Q11

Scuba divers count fin strokes to estimate the distance they have travelled under water. Felipe uses this method and a compass to swim 300 m north from the dive boat. He then turns right to `120^o`

and swim 400 m . How far from the boat is he, to the nearest metre? In what direction must Felipe swim to return to the boat?

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Q12

While standing exactly halfway between two tall trees. Nikki spots a blue jay at the top of one tree and a cardinal at the top of the other, as shown

From Nikki is pom‘t of view, the angles of elevation to the blue jay and to the cardinal are 60° and 50", respectively. The trees are 40 m apart.

a) If Nikki is 1.5 m tall, find the height of each tree.

b) How far apart are the two birds, to the nearest tenth of a metre?

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Q13

A fire station serves an area bordered by three highways that join the towns of West Port, Sackville, and Jonestown, as shown.

The fire station serves a total area of `126 km^2`

. Find the number of minutes it would take for a fire truck to drive the perimeter of this region, assuming an average speed of 80 km/h.

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Q14

From his cockpit. the pilot of a flying plane observes a jet flying
directly above an airport. as shown. From the plane, the angle of elevation to the jet is `14^o`

and the angle of depression to the airport is `38^o`

.

Find the altitude of both aircraft. to the nearest kilometre.

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Q15