Given a right triangle. anglea is 51∘. A line is drawn from anglec (90∘) to the hypotenuse, creating a 7∘ angle between the line and the cathetus adjusted to angleb. The cathetus adjusted to angel is 47cm. Find the length of the line drawn.

∠b=180∘−∠c−∠a ∠b=180∘−90∘−51∘ ∠b==46∘ Let the line be x. Use the law of Sines: sin⁡46∘47=sin⁡51∘x x=47sin⁡51∘sin⁡46∘ x≈50.8cm

Key to "Given a right triangle. anglea is 51∘. A..."

CoormaBak9

2021-09-12

Given a right triangle. anglea is

51^{\circ}

. A line is drawn from anglec

(90^{\circ})

to the hypotenuse, creating a

7^{\circ}

angle between the line and the cathetus adjusted to angleb. The cathetus adjusted to angel is 47cm. Find the length of the line drawn.

Benedict

Skilled2021-09-13Added 108 answers

∠ b = 180^{\circ} - ∠ c - ∠ a

∠ b = 180^{\circ} - 90^{\circ} - 51^{\circ}

∠ b == 46^{\circ}

Let the line be x. Use the law of Sines:

\frac{{\sin 46}^{\circ}}{47} = \frac{{\sin 51}^{\circ}}{x}

x = \frac{47 {\sin 51}^{\circ}}{{\sin 46}^{\circ}}

x \approx 50.8 c m

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