Finding Missing Sides and Angles in Right Triangles

What theorem is used to find the missing side of a right triangle when two sides are known?

• Pythagorean Theorem

• Tangent Rule

• Sine Rule

• Cosine Rule

If the hypotenuse of a right triangle is 12 and one leg is 7, what is the length of the other leg?

• √144

• 10

• √95

• 5

Which trigonometric function relates the opposite side to the hypotenuse?

• Secant

• Sine

• Cosine

• Tangent

What is the approximate measure of angle F if sin(F) = 7/12?

• 30.5 degrees

• 35.7 degrees

• 40.2 degrees

• 45.3 degrees

What is the inverse function used to find an angle when given the cosine ratio?

• Inverse Sine

• Inverse Cosine

• Inverse Tangent

• Inverse Secant

In triangle GJH, if the sides are 13 and 18, what is the tangent of angle G?

• 18/13

• 13/18

• 12/7

• 7/12

What is the length of the hypotenuse in a 30-60-90 triangle if the short leg is 249 units?

• 249 units

• 249√3 units

• 124.5 units

• 498 units

What is the angle of repose for a salt pile with a height of 4 feet and a base diameter of 10 feet?

• 38.7 degrees

• 30 degrees

• 50 degrees

• 45 degrees

If the base diameter of a salt pile is increased to 40 feet, what is the new height if the angle of repose remains the same?

• 8 feet

• 12 feet

• 16 feet

• 20 feet

At what angle should a crane's arm be set to reach a branch 90 feet high if the arm is 100 feet long and the operator is 5 feet off the ground?

• 50 degrees

• 45 degrees

• 55 degrees

• 58.2 degrees