Our eye level looking ahead is called the horizontal. Angles of Elevation and Angles of Depression angle of elevation angle of depression Horizontal (eye.

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Our eye level looking ahead is called the horizontal. Angles of Elevation and Angles of Depression angle of elevation angle of depression Horizontal (eye level) When we look down from the horizontal, we’re dealing with an angle of depression. When we look up from the horizontal, we’re dealing with an angle of elevation.

Ex. 1: A surveyor needs to know the height of a cliff. When he is 100 m horizontally out from the base of the cliff and looks up to the top of the cliff, his angle of elevation is 60 o. How tall is the cliff? Use a diagram to represent the scenario… angle of elevation Find h, the height of the cliff What ratio do we need to use? A O T Therefore, the cliff is 173 m tall.

Ex. 2: From the top of a vertical cliff that overlooks the ocean, a person measures the angle of depression of a boat at sea as 9 o. The height of the cliff is 142 m. How far is the boat from the base of the cliff? Use a diagram to represent the scenario… Find c, the distance from the boat to the base of the cliff What ratio do we need to use? T Therefore, the boat is 897 m from the base of the cliff. O A

Ex. 3: A ladder 8.6 m long is leaning against a wall. The foot of the ladder is 3.6 m from the wall. Calculate the measure of the angle formed by the ladder and the ground. Use a diagram to represent the scenario… 3.6 m 8.6 m L We want to find angle L, the angle formed by the ladder and the ground What ratio can we use? A H C Therefore, the angle formed by the ladder and the ground is 65 o.

Ex. 4: A student wants to measure the height of a rock pillar in a river. The student stands at point C in the diagram below. The angle of elevation to the top of the pillar is 28.5 o. The student then marked a line, CD, that was perpendicular to BC. The length of CD is 10 m and is 56.4 o. How tall is the rock pillar? What are we solving for? The length of AB 10 m Strategy Side AB is part of ∆ABC, but we don’t have enough information to find AB. (We need to know at least one side length in ∆ABC) ∆ABC and ∆BCD share a side (BC) We can find the length of side BC using ∆BCD. Then we can use BC and angle C to find the length of AB! WANT NEED

Ex. 4: Continued 10 m Step 1: Solve for BC using ∆BCD Step 2: Use BC to solve for AB What ratio do we need to use? A O T A O T Therefore, the rock pillar is 8.2 m tall.