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Algebra 2
Name 
qquad Elizabeth
Torres
Right Triangles
Date 
qquad 
Pe
Find the measure of each side indicated. Round to the nearest tenth.
1)

{:[sin 52=(13 )/(x)],[x*7881(13 )/(x)*x],[(7881)/(7881)=(13)/(7881)],[x=16.49]:}

Algebra 22\newlineName \qquad Elizabeth\newlineTorres\newlineRight Triangles\newlineDate \qquad Pe \mathrm{Pe} \newlineFind the measure of each side indicated. Round to the nearest tenth.\newline11)\newlinesin52=13xx788113xx78817881=137881x=16.49 \begin{array}{l} \sin 52=\frac{13}{x} \\ x \cdot 7881 \frac{13}{x} \cdot x \\ \frac{7881}{7881}=\frac{13}{7881} \\ x=16.49 \end{array} \newline33)\newline55)\newline77)\newline99)\newline22)\newline44)\newline66)\newline88)\newline1010)

Full solution

Q. Algebra 22\newlineName \qquad Elizabeth\newlineTorres\newlineRight Triangles\newlineDate \qquad Pe \mathrm{Pe} \newlineFind the measure of each side indicated. Round to the nearest tenth.\newline11)\newlinesin52=13xx788113xx78817881=137881x=16.49 \begin{array}{l} \sin 52=\frac{13}{x} \\ x \cdot 7881 \frac{13}{x} \cdot x \\ \frac{7881}{7881}=\frac{13}{7881} \\ x=16.49 \end{array} \newline33)\newline55)\newline77)\newline99)\newline22)\newline44)\newline66)\newline88)\newline1010)
  1. Set up equation: First, let's set up the equation using the definition of sine in a right triangle: sin(52)=oppositehypotenuse\sin(52^\circ) = \frac{\text{opposite}}{\text{hypotenuse}}.
  2. Solve for x: So we have sin(52)=13x\sin(52^\circ) = \frac{13}{x}. We need to solve for xx.
  3. Multiply and isolate xx: To solve for xx, multiply both sides of the equation by xx to get xsin(52°)=13x \cdot \sin(52°) = 13.
  4. Calculate sin(52°)\sin(52°): Now, divide both sides by sin(52°)\sin(52°) to isolate xx: x=13sin(52°)x = \frac{13}{\sin(52°)}.
  5. Plug in sin(52°)\sin(52°): Use a calculator to find sin(52°)\sin(52°), which is approximately 0.78800.7880 (rounded to four decimal places).
  6. Perform division: Now, plug in the value of sin(52°)\sin(52°) into the equation: x=130.7880x = \frac{13}{0.7880}.
  7. Perform division: Now, plug in the value of sin(52°)\sin(52°) into the equation: x=130.7880x = \frac{13}{0.7880}.Perform the division to find xx: x16.5x \approx 16.5 (rounded to the nearest tenth).