8.5 Solving Acute Triangle Problems
Chapter
Chapter 8
Section
8.5
Solutions 26 Videos

Explain how you would determine the measurement of the indicated angle or side in each triangle.

0.35mins
Q1a

Explain how you would determine the measurement of the indicated angle or side in each triangle.

0.23mins
Q1b

Explain how you would determine the measurement of the indicated angle or side in each triangle.

0.09mins
Q1c

Determine the measurements of the indicated angles and sides.

0.40mins
Q2a

Determine the measurements of the indicated angles and sides.

0.16mins
Q2b

Determine the measurements of the indicated angles and sides.

0.41mins
Q2c

The angle between two equal sides of an isosceles triangle is 52^o.

Each of the equal sides is 18 cm long.

• Determine the measures of the two equal angles in the triangle.
0.45mins
Q3a

The angle between two equal sides of an isosceles triangle is 52^o.

Each of the equal sides is 18 cm long.

• Determine the length of the third side.
0.56mins
Q3b

The angle between two equal sides of an isosceles triangle is 52^o.

Each of the equal sides is 18 cm long.

• Determine the perimeter of the triangle.
0.26mins
Q3c

A boat leaves Oakville and heads due east for 5.0 km as shown in the diagram at the left. At the same time, a second boat travels in a direction S60°E From Oakville for 4.0 km. How far apart are the boats when they reach their respective destinations?

0.36mins
Q4

A radar operator on a ship discovers a large sunken vessel lying flat on the ocean floor, 200 m directly below the ship. The radar operator measures the angles of depression to the front and back of the sunken ship to be 56° and 62°. How long is the sunken ship?

1.40mins
Q5

The base of a roof is 12.8 m wide as shown in the diagram at the left. The rafters form angles of 48° and 44° with the horizontal. How long, to the nearest tenth of a metre, is each rafter?

1.12mins
Q6

A flagpole stands on top of a building that is 27 m high. From a point on the ground some distance away, the angle of elevation to the top of the flagpole is 43". The angle of elevation to the bottom of the flagpole is 32°.

a) How far is the point on the ground from the base of the building?

b) How tall is the flagpole?

1.38mins
Q7

Two ships, the Albacore and the Bonito, are 50 km apart. The Albacore is N45°W of the Bonito. The Albacore sights a distress flare at 55°E. The Bonito sights the distress flare at 550°W. How far is each ship from the distress flare?

2.52mins
Q8

Fred and Agnes are 520 m apart. As Brendan flies overhead in an airplane, they measure the angle of elevation of the airplane. Fred measures the angle of elevation to be 63°. Agnes measures it to be 36°. What is the altitude of the airplane?

1.55mins
Q9

The Nautilus is sailing due east toward a buoy. At the same time, the Porpoise is approaching the buoy heading N42°E. If the Nautilus is 5.4 km from the buoy and the Porpoise is 4.0 km from the Nautilus. on a heading of 546°E, how far is the Porpoise from the buoy?

1.43mins
Q10

Two support wires are fastened to the top of a satellite dish tower from points A and B on the ground, on either side of the tower. One wire is 18 m long, and the other wire is 12 m long. The angle of elevation of the longer wire to the top of the tower is 38°.

• How tall is the satellite dish tower?
1.41mins
Q11a

Two support wires are fastened to the top of a satellite dish tower from points A and B on the ground, on either side of the tower. One wire is 18 m long, and the other wire is 12 m long. The angle of elevation of the longer wire to the top of the tower is 38°.

• How far apart are points A and B?
1.24mins
Q11b

A regular pentagon is inscribed in a circle with radius 10 cm as shown in the diagram below. Determine the perimeter of the pentagon.

1.44mins
Q12

Ryan is in a police helicopter 400 m directly above a highway. When he looks west, the angle of depression to a car accident is 65°. When he looks east, the angle of depression to the approaching ambulance is 30°.

• How far away is the ambulance from the scene of the accident?
2.07mins
Q13a

Ryan is in a police helicopter 400 m directly above a highway. When he looks west, the angle of depression to a car accident is 65°. When he looks east, the angle of depression to the approaching ambulance is 30°.

• The ambulance is travelling at 80 km/h. How long will it take the ambulance to reach the scene of the accident?
0.52mins
Q13b

The radar screen in an air—traffic control tower shows that two airplanes are at the same altitude. According to the range finder, one airplane is 100 km away, in the direction N60°E. The other airplane is 160 km away, in the direction S5O°E.

• How far apart are the airplanes?
1.31mins
Q14a

The radar screen in an air—traffic control tower shows that two airplanes are at the same altitude. According to the range finder, one airplane is 100 km away, in the direction N60°E. The other airplane is 160 km away, in the direction S5O°E.

• If the airplanes are approaching the airport at the same speed, which airplane will arrive first?
0.21mins
Q14b

In a parallelogram, two adjacent sides measure 10 cm and 12 cm. The shorter diagonal is 15 cm. Determine, to the nearest degree, the measures of all four angles in the parallelogram.

2.08mins
Q15

From the top of a bridge that is 50 m high, two boats can be seen anchored in a marina, One boat is anchored in the direction 820°W, and its angle of depression is 40°. The other boat is anchored in the direction 560°E, and its angle of depression is 30°. Determine the distance between the two boats.

Two paper strips, each 5 cm wide, are laid across each other at an angle of 30°, as shown at the right. Determine the area of the overlapping region. Round your answer to the nearest tenth of a square centimetre.