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Consider a triangle ABC
like the one below. Suppose that a=34, b=53, and c=74.
The figure is not drawn to scale.) Solve the triangle.
Carry your intermediate computations to at least four decimal places, and round your answers to the nearest tenth.

If there is more than one solution, use the button labeled "or".

Consider a triangle ABC like the one below Suppose that a34 b53 and c74 The figure is not drawn to scale Solve the triangle Carry your intermediate computation class=

Respuesta :

meeraasrinivas

Answer:

A =24.7° ; B = 40.6° ; C =114.7°

Step-by-step explanation:

Cosine Law

a² = b²+c²-2bc cos A

b² = c²+a² -2ca cos B

Sum of three angles of a triangle is 180°.

a = 34 ; b= 53; c = 74

Substituting the given values in the cosine law, we have

34² = 53² + 74² - 2*53 *74 * cos A

7844 cos A = 2809 + 5476 - 1156 = 7129

cos A = 7129/7844 = 0.9088

A = cos⁻¹ (0.9088) = 24.6600° = 24.7°

53² = 74² + 34² - 2 (74)(34) cos B

5032 cos B = 5476 + 1156 - 2809 = 3823

cos B = 3823/5032 = 0.7597

B = cos⁻¹ (0.7597) = 40.5622° = 40.6°

Also, A + B + C = 180°

24.7 + 40.6 + C =180

C =180 -  65.3 = 114.7°

∴ A =24.7° ; B = 40.6° ; C =114.7°
A=24.7
B=90.1
C=65.2A=24.7°;B=90.1°;C=24.7°

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