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What information do you need to know about an acute triangle to use the sine law?

Determine the length of f to the nearest tenth of a centimetre.

Determine the measure of ÐR to the nearest degree.

Determine the measure of q to the nearest degree.

In DDEF, ÐD = 61°, d = 23.9 cm, and ÐE = 38°.
Determine the length of side e to the nearest tenth of a centimetre.

What information do you need to know about an acute triangle to use the cosine law?

Determine the length of EF to the nearest centimetre.

Determine the length of KL to the nearest centimetre.

Determine the length of PQ to the nearest tenth of a centimetre.

In DPQR, r = 52.5 cm, p = 40.0 cm, and ÐQ = 67°.
Determine the measure of q to the nearest tenth of a centimetre.

In DDEF, d = 23.9 cm, e = 16.8 cm, and f = 27.0 cm.
Determine the measure of ÐF to the nearest degree.

Which one of the following equations is valid?

Which pair of angles have the tangent ratio 0.60?

Which law could you use to determine the unknown angle in this triangle?

Determine the unknown angle to the nearest degree.

Determine the unknown side length to the nearest centimetre.

In DCDE, DE = 9.0 cm and ÐD = 59°.
What is the height of the triangle from base DC?

Which would you use to determine the indicated angle measure?

Which would you use to determine the indicated angle measure?

In DRST, the values of s and ÐT are known. What additional information do you need to know if you want to use the sine law to solve the triangle?

In DLMN, l = 10.0 cm, m = 13.2 cm, and ÐM = 79°.
Determine the measure of ÐL to the nearest degree.

A radar operator on a ship discovers a large sunken vessel lying parallel to the ocean surface, 180 m directly below the ship. The length of the vessel is a clue to which wreck has been found. The radar operator measures the angles of depression to the front and back of the sunken vessel to be 52° and 67°. How long, to the nearest tenth of a metre, is the sunken vessel?

In a parallelogram, two adjacent sides measure 8.4 cm and 7.2 cm. The shorter diagonal is 10.5 cm. Determine, to the nearest degree, the measures of the larger angles in the parallelogram.

What law or property would you use to determine the indicated side length?

Two Jasper National Park rangers in their fire towers spot a fire.
Determine the distances, to the nearest tenth of a kilometre, from each tower to the fire. Show your work.

The pendulum of a grandfather clock is 85.0 cm long. When the pendulum
swings from one side to the other side, it travels a horizontal distance of 10.5 cm.
Determine the angle through which the pendulum swings. Round your answer to the nearest tenth of a degree.

Two airplanes leave Dawson City Airport at the same time.
One airplane travels at 420 km/h. The other airplane travels at 375 km/h.
About 2 h later, they are 1000 km apart. Determine the angle between their paths,
to the nearest degree.

A radio tower is supported by two wires on opposite sides. On the ground,
the ends of the wire are 46.5 m apart. One wire makes a 62° angle with the ground. The other makes a 68° angle with the ground.
Draw a diagram of the situation. Then, determine the height of the tower to the nearest tenth of a metre.

A surveyor is measuring the length of a lake. He takes angle measurements from two positions, A and B, that are 395 m apart, and on opposite sides of the lake. From B, the measure of the angle between the sight lines to the ends of the lake is 132°, and the measure of the angle between the sight lines to A and one end of the lake is 111°. From A, the measure of the angle between the sight lines to the ends of the lake is 65°, and the measure of the angle between the sight lines to B and the same end of the lake is 23°. Calculate the length of the lake, to the nearest metre. Show your work.