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Worksheet: Finding Angles Using the Sine and Cosine Ratios

Q1:

Find the measure of giving the answer to the nearest second.

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Q2:

Find the measure of giving the answer to the nearest second.

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Q3:

In the given figure, find the measure of angle , in degrees, to two decimal places.

Q4:

The height of a ski slope is 16 meters and the length is 20 meters. Find the measure of giving the answer to two decimal places.

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Q5:

Find giving the answer to the nearest second.

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Q6:

Find giving the answer to the nearest second.

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Q7:

Find the measure of given is a rectangle where and . Give the answer to the nearest second.

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Q8:

Find the measure of given is a rectangle where and . Give the answer to the nearest second.

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Q9:

Find the measure of , given is an isosceles trapezium where and giving the answer to the nearest second.

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Q10:

Find the measure of , given is an isosceles trapezium where and giving the answer to the nearest second.

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Q11:

A car is going down ramp which is 10 metres high and 71 metres long. Find the angle between the ramp and the horizontal giving the answer to the nearest second.

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Q12:

The base of a truck is 2 feet off the ground and a 20-foot ramp is used to load the truck. Find the angle the ramp makes with the horizontal ground.

Q13:

A car is going down ramp which is 4 metres high and 43 metres long. Find the angle between the ramp and the horizontal giving the answer to the nearest second.

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Q14:

A palm tree snaps due to bad winds. The vertical trunk is 5 metres tall and the inclined part is 6 metres. Find the measure of the angle between the inclined part and the ground giving the answer to the nearest second.

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Q15:

A builder leans a 6-foot plank of wood against a vertical wall. If one end of the plank is 1.5 feet from the bottom of the wall, what is the angle between the plank and the wall?