Give exact answers where possible and round all approximations to the nearest hundredth unless otherwise specified.
1) Solve for \(x\) and \(y\) in the triangle below.
2) Solve for \(x\) and \(y\) in the triangle below.
3) List all six trigonometric ratios of \(\theta\) and \(\phi\).
4) In a right triangle, \(\sin \theta = \frac{4}{5}\). Find the other five trigonometric values of \(\theta\).
5) In a right triangle, the length of the shorter leg is \(4\) and the hypotenuse is \(8\). Find the measure of both acute angles in the triangle.
6) Find the exact value of \(x\) and \(y\).
7) Find the exact value of \(x\) and \(y\).
8) The altitude of an equilateral triangle is \(5 \sqrt{3}\), find the perimeter of the triangle.
9) The diagonal of a square is \(9 \sqrt{2}\), find the area of the square.
10) Find the measure of \(\theta\) to the nearest tenth of a degree.
11) Find the measure of \(\theta\) to the nearest tenth of a degree.
12) In \(\triangle XYZ\), \(XY=3\), \(\angle Y = 90^{\circ}\), and \(\angle X = 22^{\circ}\). Solve the triangle.
13) If \(\cos \theta = c\) where \(\theta\) is an acute angle, then what is \(\sin(90^{\circ} - \theta)\)?
14) Leighton is standing at the top of a building that is \(43\) feet high. She is looking at a fire hydrant that is \(75\) feet away from the base of the building. If her eyes are \(4\) feet above the rooftop, what is the angle of depression from her eyes to the fire hydrant?
15) An engineer is making plans for a new handicap access ramp. Safety regulations state that such a ramp cannot have an angle of elevation exceeding \(5^{\circ}\). If the entrance that the ramp is being built up to is \(4\) feet off the ground what is the minimum length of the horizontal base of the ramp that the engineer can build?
Review
16) Solve the following equation \(\left(\Large\frac{1}{3}\right)^{2x} = \;9^{x-1}\).
17) Find the inverse of \(f(x)=(x-1)^2-3\) where Dom \(f = \{x:x \geq 1 \}\).
18) The fourth term of an arithmetic sequence is \(8\) and the \(13\)th term of the same sequence is \(71\). Find the \(100\)th term of the sequence.
19) Find the sum of the first \(20\) terms of the sequence described in the previous problem.
20) Condense the logarithm, \(3\log_{b} a - 6\log_{b} a\).
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