Lesson: The Tangent Ratio

Find the values of and giving your answer to the nearest second.

Find the values of and giving your answer to the nearest second.

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

is a right-angled triangle at , where and . Find the measure of giving the answer to the nearest second.

is a right-angled triangle at , where and . Find the measure of giving the answer to the nearest second.

A building is 8.78 km tall from the ground. The angle of elevation of the top of the building from a point on the ground is . Find the distance between the point on the ground and the top of the building giving the answer to the nearest metre.

What percentage grade should a road have if the angle of elevation of the road is 4 degrees? The percentage grade is defined as the change in the altitude of the road over a 100-foot horizontal distance. For example, a grade means that the road rises 5 feet for every 100 feet of horizontal distance.

A lighthouse with a height of 89 metres is constructed on a cliff. From a boat in the sea, the angle of elevation to the top of the lighthouse is , and the angle of elevation to the base of the lighthouse is . Find the height of the cliff from sea level giving the answer to the nearest metre.

From the top of a house 15 m tall, the angles of elevation and depression of the top and the base of a building are and respectively. Find the height of the building giving the answer to the nearest metre.

The dimensions of a rectangular garden is 20 meters by 17 meters. Triangle represents the lawn where . Find the value of giving the answer to the nearest second.