Questions
Find the indicated unknowns. Each problem refers to the triangle shown above where the bottom right angle is 90 degrees!
Important Note: Give exact answers, using fractions or square roots (e.g. sqrt(3)/2) if necessary.
If $a = \sqrt{21}$ and $b = 2$, then $sin(\beta) = $ ??, $cos(\beta) = $ ??, and $tan(\beta) = $ ??
If $a = 3$ and $c = 4$, then $sin(\beta) = $ ??, $cos(\beta) = $ ??, and $tan(\beta) = $ ??
If $a = \sqrt{3}$ and $b = 1$, then $sin(\alpha) = $ ??, $cos(\alpha) = $ ??, and $tan(\alpha) = $ ??
If $b = 1$ and $c = \sqrt{2}$, then $sin(\beta) = $ ??, $cos(\beta) = $ ??, and $tan(\beta) = $ ??
If $a = 12$ and $c = 13$, then $sin(\alpha) = $ ??, $cos(\alpha) = $ ??, and $tan(\alpha) = $ ??
If $a = 3$ and $c = 5$, then $sin(\alpha) = $ ??, $cos(\alpha) = $ ??, and $tan(\alpha) = $ ??
Important Note: For the next three questions, evaluate any expressions involving trigonometric functions in your answers. Give exact answers, using
fractions or square roots (e.g. sqrt(3)/2) if necessary.
If $c = 16$ and $\beta = 30^\circ$, then $a = $ ??
If $c = 25$ and $\alpha = 45^\circ$, then $b = $ ??
If $b = 6$ and $\beta = 60^\circ$, then $a = $ ??
A climber who needs to estimate the height of a cliff stands at a point on the ground $a = 9$ metres from the base of the cliff and estimates that the angle of
elevation to the top of the cliff is $72^\circ$. Assuming that the cliff is perpendicular to the ground, find the approximate height of the cliff. (Express your answer to
the nearest tenth.)
Answer
