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The measure of 3 angles in a triangle are in a 1:2:3 ratio. What is the measure of the middle angle?

A 17 ft ladder is propped against a 15 ft wall. What is the degree measurement between the ladder and the ground?

Explanation:

Since all the answer choices are in trigonometric form, we know we must not necessarily solve for the exact value (although we can do that and calculate each choice to see if it matches). The first step is to determine the length of the ground between the bottom of the ladder and the wall via the Pythagorean Theorem: “x2 + 152 = 172”; x = 8. Using trigonometric definitions, we know that “opposite/adjecent = tan(theta)”; since we have both values of the sides (opp = 15 and adj = 8), we can plug into the tangential form tan(theta) = 15/8. However, since we are solving for theta, we must take the *inverse* tangent of the left side, “tan-1”. Thus, our final answer is

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### Example Question #51 : Plane Geometry

What is the sine of the angle between the base and the hypotenuse of a right triangle with a base of 4 and a height of 3?

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Explanation:

By rule, this is a 3-4-5 right triangle. Sine = (the opposite leg)/(the hypotenuse). This gives us 3/5.

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### Example Question #3 : How To Find An Angle In A Right Triangle

In a right triangle ABC, the measure of angle C is greater than 60 degrees. Which of the following statements could describe the measures of angles A and B?

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