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Find the missing length of the triangle.



a= in.

Find the missing length of the triangle. a= in.-example-1
User Tmaric
by
8.7k points

2 Answers

2 votes

Answer:

a = 11.9883 in

Explanation:

Sides:

a = 5.6 in

b = 11.9883 in

c = 10.6 in

Angles:

A = 27.8476 °

B = 90 °

C = 62.1524 °

Other:

P = 28.1883 in

s = 14.0942 in

K = 29.68 in2

r = 2.10584 in

R = 5.99416 in

SAS is Side, Angle, Side

Given the size of 2 sides (c and a) and the size of the angle B that is in between those 2 sides, you can calculate the sizes of the remaining 1 side and 2 angles. Use The Law of Cosines to solve the remaining side.

Law of Cosines

If a, b and c are the lengths of the legs of a triangle opposite to the angles A, B and C respectively; then the law of cosines states:

a^2 = c^2 + b^2 - 2bc cos A, solving for cos A, cos A = ( b^2 + c^2 - a^2 ) / 2bc

b^2 = a^2 + c^2 - 2ca cos B, solving for cos B, cos B = ( c^2 + a^2 - b^2 ) / 2ca

c^2 = b^2 + a^2 - 2ab cos C, solving for cos C, cos C = ( a^2 + b^2 - c^2 ) / 2ab

Solving, for example, for an angle, A = cos^-1 [ ( b^2 + c^2 - a^2 ) / 2bc ]

User Jpmcosta
by
8.6k points
2 votes

Answer:

9 in.

Explanation:

a^2 + 5.6^2 = 10.6^2

a^2 + 31.36 = 112.36

Subtract 31.36 from both sides

a^2 = 81

Squart Root both sides

a = 9 inches

User Moria
by
8.4k points

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