How do you solve the triangle given B = 18°, C = 113°, b = 44?

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Answer 1 · 2016-02-21T20:03:50

First, draw a diagram to represent the situation.

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Let's start easy, by finding the measure of angle A.

The angles in a triangle add up to 180.

$A = 180 - 113 - 18$

$A = 49˚$

Now, we must find sides a and c. We can do this by Sine's Law:

$(sinA)/a = (sinB)/b = sinC/c$

$(sin49)/a = (sin18)/44 = (sin113)/c$

Start by solving for a (with a scientific calculator)

$a = (sin49 xx 44)/sin18$

$a ~= 107.46$

Next we can solve for c.

$c = (sin113 xx 44)/sin18$

$c ~= 131.07$

So, $A = 49˚, a ~=107.46 and c ~= 131.07$

Practice exercises:

a) $A = 58˚, b = 52 cm and B = 71˚$

b) $A = 122˚, a = 98 ft. and C = 10˚$

Good luck!