What is the length of side ad? . . 6 cm. 8.5 cm. 10.4 cm. 12 cm

The length of side AD is 6 cm.

We solve this problem using the principle of trigonometric ratio.

Look at the figure.  

Given that the triangle ABC is right-angled at B

We start from this statement:

“sum of measures of angles in a triangle is 180°.”

In the triangle ABC:

∠A + ∠B + ∠C = 180°

∠A + 90° + 30° = 180°

∠A + 120° = 180°

∠A = 180° - 120°

∠A = 60°

See the picture again. The triangle ABD is a right angle at D.  

About angle D:

Based on trigonometric ratios, the relationship between AD, AB, and angle A is as follows:

We get the length of AD is 6 cm.

Note:

Keywords: the length, side AD, right-angled, adjacent, hypotenuse, opposite, sin, cos, tan, sum of measures of angles in triangle are 180°, 30°, 60°

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