Question

10 sur 20
quelle est la valeur de la mesure du côté a ?
triangle with right angle, 20 cm vertical leg, 20° angle at base, hypotenuse a
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a 58,5 cm
b aucune de ces réponses
c 21,3 cm
d 54,9 cm
e 0,017 cm
f 0,046 cm

Explanation:

Step1: Identify the trigonometric relation

In a right - triangle, we know that \(\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}\) and \(\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}\), \(\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}\). Here, the side of length \(20\) cm is opposite to the \(20^{\circ}\) angle? No, wait, the right - angle is at the bottom - left, the vertical side is \(20\) cm, the angle at the bottom - right is \(20^{\circ}\). So the vertical side (length \(20\) cm) is opposite to the \(20^{\circ}\) angle? No, the angle at the bottom - right is \(20^{\circ}\), so the adjacent side to \(20^{\circ}\) is the horizontal leg, the opposite side is the vertical leg (\(20\) cm), and the hypotenuse is \(A\). We use the sine function: \(\sin(20^{\circ})=\frac{\text{opposite}}{\text{hypotenuse}}=\frac{20}{A}\)

Step2: Solve for \(A\)

We can re - arrange the formula \(\sin(20^{\circ})=\frac{20}{A}\) to get \(A = \frac{20}{\sin(20^{\circ})}\)

We know that \(\sin(20^{\circ})\approx0.3420\)

Then \(A=\frac{20}{0.3420}\approx58.5\) cm

Answer:

A. 58,5 cm