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Consider a right triangle with leg b = 7.1 and opposite angle B = 39.3. Using a calculator, determine the other angle and the remaining sides of the triangle. Express your answers using at least one decimal place.

User Hornetbzz
by
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1 Answer

5 votes

Answer:

i. a = 8.7, b = 7.1 and c = 11.2

ii. A =
50.7^(o), B =
39.3^(o) and C =
90^(o)

Explanation:

Given a right triangle with, b = 7.1 and B =
39.3^(o).

I. Applying the trigonometric function to determine leg a, we have;

Tan θ =
(opposite)/(adjacent)

Tan
39.3^(o) =
(7.1)/(a)

a =
(7.1)/(Tan 39.3^(o) )

= 8.675

The length of leg a is 8.7.

ii. To determine leg c,

Sin
39.3^(o) =
(opposite)/(hypotenuse)

=
(7.1)/(c)

⇒c =
(7.1)/(Sin39.3^(o) )

= 11.21

The length of leg c is 11.2.

iii. Given that: B =
39.3^(o) and C =
90^(o)

Then,

A + B + C =
180^(o) (sum of angles at a point)

A +
39.3^(o) +
90^(o) =
180^(o)

A +
129.3^(o) =
180^(o)

A =
180^(o) -
129.3^(o)

=
50.7^(o)

User Nakeia
by
7.9k points

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