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this is one of my homework problems, please help me solve the triangle if you can! (Rounding the side lengths to the nearest tenth and the angles to the nearest degree)

This Is One Of My Homework Problems Please Help Me Solve The Triangle If You Can Rounding The Side Lengths To The Nearest Tenth And The Angles To The Nearest De class=

Sagot :

1. Finding the missing side of triangle∆ ABC

• We are given two sides b = 4 and c = 8 with an angle A =46° between the two sides .

,

• we are to find side a =?? and angle B and C

2. Apply the Cosine rule of triangle

a^2 = b^2 + c^2 -2bc Cos A

a^2 = 4^2 + 8^2 -2*4*8 Cos46°

a^2 = 16 +64 -64(0.695)

a^2 = 80 -44.46

a^2 =35.54

a = (√35.54)

a = 5.962......( round off to the nearest tenth)

Therefore , a = 6

3. solving angle B

tan B = opp/adj = b/a = 4/6 =0.66666

tan^-1( 0.66666) = angle B T

Therefore, angle B = 33.68 ≈34°

4 . Solving Angle C

angle A + angle B + angle C = 180° ( angles of a triangle add up to 180°)

46 + 34 + angle C = 180°

angle C= 180 ° -80°

Therefore, angle C = 100°

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