Right Triangle Trigonometry

Pre-CalculusLesson 4.3

sin = __________

csc = __________

cos =__________

sec =__________

tan =__________

cot =__________

Recall: “Some old hippie caught another hippie tripping over apples.”

Evaluate all six trig functions.

θ

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TRIGONOMETRIC IDENTITIES

Let θ be an acute angle such that sin θ = 0.6. Find the value of: 1) cos θ 2) tan θ

Let θ be an acute angle such that tan θ = 3. Find the value of:3) cot θ 4) sec θ

The angle of elevation represents the angle from the horizontal upward to an object.

The angle of depression represents the angle from the horizontal downward to an object.

Due to the z-property, we will label both as the bottom acute angle in our triangles.

5) A surveyor is standing 115 feet from the base of the Washington Monument. The surveyor measures the angle of elevation to the top of the monument as 78.3°. How tall is the Washington Monument?

6) You are 200 yards from a river. Rather than walking directly to the river, you walk 400 yards along a straight path to the river’s edge. Find the acute angle θ between this path and the river’s edge.

7) Specifications for a loading ramp require a rise of 1 foot for each 3 feet of horizontal length. Find the length of the dock and the angle of elevation if the top of the ramp is 4 feet above the ground.

8) A plane takes off and flies at an angle of 10° off the runway. When the airplane is 500 feet high, find the distance, to the nearest foot, that the plane has traveled.