Question 1
From the top of a 50-foot cliff, the angle of depression to a boat on the water is 30°. How far is the boat from the base of the cliff, in feet?
Hard - Quiz 1
Solve angle-of-depression problems, work with two-triangle setups, apply the Pythagorean identity, extend to three dimensions, and combine trig with algebra.
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A person standing at point \(A\) measures the angle of elevation to the top of a tower as 30°. After walking 40 feet closer to the tower to point \(B\), the angle of elevation is 60°. What is the height of the tower, in feet?
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Answer question 2 to unlock
In a right triangle, \(\sin(\theta) = \dfrac{3}{5}\) and \(\theta\) is an acute angle. What is the value of \(\cos(\theta)\)?
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A rectangular box has a length of 6 inches, a width of 8 inches, and a height of 10 inches. What is the length of the space diagonal (the diagonal from one corner to the opposite corner through the interior of the box)?
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Answer question 4 to unlock
In right triangle \(ABC\) with the right angle at \(C\), \(\sin(A) = \dfrac{x + 1}{10}\) and \(\cos(A) = \dfrac{2x - 2}{10}\). What is the value of \(x\)?