Question

In AGHI, h = 91 inches, g = 88 inches and LG-75°. Find all possible values of ZH, to the

nearest 10th of a degree.

Answer 1

The measure of the angle ∠G nearest to tenth place will be 77.1°. The law of sines can be used to find the missing dimensions of a triangle with two sides and a non-included angle given.

Step-by-step explanation:

What is the cosine law?

The squared of the size of any solitary side of either a triangle is equal, by the cosine rule, to the total of the squares of the lengths of the other two sides, times by the cosine of something like the angle they are a part of.

Let the triangle ΔABC, then the cosine law is given as,

c² = a² + b² - 2 a·b cos C

In ΔGHI, g = 91 cm, h = 73 cm and i = 73 cm. Then the measure of the angle ∠G is given as,

g² = h² + i² - 2 h·i cos G

(91)² = (73)² + (73)² - 2 x 73 x 73 cos G

8281 = 5329 + 5329 - 10658 cos G

10658 cos G = 5329 + 5329 - 8281

10658 cos G = 2377

cos G = 0.223

cos G = cos 77.1°

The measure of the angle ∠G nearest to tenth place will be 77.1°.

In AGHI, h = 91 inches, g = 88 inches and LG-75°. Find all possible values of ZH, to the nearest 10th of a degree?

Answer 2

• 87.3°
• 92.7°

Step-by-step explanation:

You want the possible values of ∠H in ∆GHI with g=88 in, h=91 in, ∠G=75°.

Law of sines

The law of sines can be used to find the missing dimensions of a triangle with two sides and a non-included angle given. When the given angle is acute and opposite the shortest of the given sides, there may be two solutions.

sin(H)/h = sin(G)/g

H = arcsin(h/g·sin(G)) ≈ 87.3°

Angles x and 180°-x have the same sine, so another possibility for angle H is ...

H = 180° -87.3° = 92.7°

Angle H may be 87.3° or 92.7°.

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