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Chapter 8: Problem 3
Simplify. $$\sqrt{45}$$
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Prove: If \(R\) is any acute angle, \((\sin R)^{2}+(\cos R)^{2}=1 .\) (Hint: From any point on one side of \(\angle R,\) draw a perpendicular to the other side.
An altitude of an equilateral triangle has length \(6 \sqrt{3} .\) What is the perimeter of the triangle?
A natural question to consider is the following: Does \(\tan A+\tan B=\tan (A+B) ?\) Try substituting \(35^{\circ}\) for \(A\) and \(25^{\circ}\) for \(B\). a. \(\tan 35^{\circ}+\tan 25^{\circ} \approx ?+?=?\) b. \(\tan \left(35^{\circ}+25^{\circ}\right)=\tan ?^{\circ} \approx ?\) c. What is your answer to the general question raised in this exercise, yes or no? d. Do you think \(\tan A-\tan B=\tan (A-B) ?\) Explain.
In \(\triangle A B C, m \angle B=m \angle C=72\) and \(B C=10\) a. Find \(A B\) and \(A C\) b. Find the length of the bisector of \(\angle A\) to \(\overline{B C}\).
Simplify. $$\sqrt{54}$$
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