In \Delta ABC, the side lengths are given as a = 7\text{ cm}, b = 5\text{ cm}, and c = 3\t… — JAMB UTME

In $\Delta ABC$ , the side lengths are given as $a = 7\text{ cm}$ , $b = 5\text{ cm}$ , and $c = 3\text{ cm}$ . What is the measure of angle $A$ in degrees?

Answer: 120 degrees

Answer

The measure of angle

A

120^\circ

Using the Cosine Rule formula

\cos A = \frac{b^2 + c^2 - a^2}{2bc}

, substituting

a = 7

b = 5

, and

c = 3

yields

\cos A = \frac{25 + 9 - 49}{30} = -\frac{1}{2}

. The inverse cosine of

-\frac{1}{2}

gives an obtuse angle of

120^\circ

Step-by-Step Solution

Apply the Cosine Rule for an unknown angle in terms of the three sides

\cos A = \frac{b^2 + c^2 - a^2}{2bc}

When all three side lengths of a non-right triangle are given (SSS), the Cosine Rule is required to solve for any internal angle.

Substitute

a = 7

b = 5

, and

c = 3

into the Cosine Rule formula and evaluate

\cos A = \frac{25 + 9 - 49}{2 \times 5 \times 3} = \frac{-15}{30} = -0.5

Evaluating the terms in the numerator and denominator simplifies the expression for

\cos A

Calculate the inverse cosine of

-0.5

to find angle

A

A = 120^\circ

Since the cosine value is negative, angle

A

is obtuse and lies in the second quadrant (

90^\circ < A < 180^\circ

Key Concept

Using the Cosine Rule with three side lengths (SSS) to find an obtuse interior angle

Estimated Time:1m 30s

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