+2446 Use the trigonometric ratios to find the height of the building:
| \(\frac{\tan 53}{1}=\frac{x}{30}\) | The tangent trigonometric ratio compares the opposite angle and the adjacent angle. Cross multiply to isolate x. |
| \(30\tan 53ft=x\) | Use a calculator to approximate the height of the building |
| \(30 \tan(53)\approx39.8113ft\) | Of course, leave units in your final answer! |
One last note before you go!
Be sure that your calculator is in degree mode when doing this calculation!
+2446
\(99.\overline{9999}=100\) This statement to my left is actually true. Let's prove that by manipulating the number:
| \(99.\overline{9999}=x\) | I'll set it equal to some number. Multiply both sides by 10 |
| \(999.\overline{9999}=10x\) | This might be the hardest step to understand. Subtract x on both sides! |
| \(999.\overline{9999}-99.\overline{9999}=10x-x\) | Simplify both sides of the equation |
| \(900=9x\) | Divide by 9 on both sides |
| \(100=x\) | |
WOAH! \(99.\overline{9999}=100\). It's kind of disguised, isn't it?
+9491 Rarinstraw's answer is correct if the triangle is a right triangle with C as the 90º angle, but if the triangle is not a right triangle, you can use the Law of Sines to find other two lengths.
The Law of Sines says:
\(\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}\)
where A , B , and C are angles, and a , b , and c , are sides across from their respective angles.
This might help: https://www.mathsisfun.com/algebra/trig-sine-law.html 
+2446 | Statements | Reasons |
| \(\angle RST\cong\angle XYZ\) | Corresponding angles in similar triangles are congruent |
| \(m\angle RST=m\angle XYZ\) | Congruent angles have the same measure, by definition. |
| \(23^{\circ}=m\angle{XYZ}\) | Substitution property of equality OR Transitive property of equality. |
| \(m\angle{XYZ}+m\angle{YZX}+m\angle{ZXY}=180^{\circ}\) | Triangle sum therom (The sum of the interior angles of triangle is 180) |
| \(23^{\circ}+47^{\circ}+m\angle{ZXY}=180^{\circ}\) | Substitution property of equality |
| \(70^{\circ}+m\angle{ZXY}=180^{\circ}\) | Simplify |
| \(m\angle{ZXY}=110^{\circ}\) | Subtraction property of equality |
Thus, \(m\angle{X}=110^{\circ}\)
.
