The length of side AD is 6 cm.
[tex]\boxed{ \ The \ Answer \ is \ A \ }[/tex]
Further explanation
We solve this problem using the principle of trigonometric ratio.
Look at the figure.
Given that the triangle ABC is right-angled at B
- Length of AB = 12 cm
- ∠ C = 30°
- The segment of BD is perpendicular to AC side.
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:
- AB is the hypotenuse
- AD is the adjacent side
Based on trigonometric ratios, the relationship between AD, AB, and angle A is as follows:
[tex]\boxed{ \ cos \ A = \frac{adjacent}{hypotenuse} \ }[/tex]
[tex]\boxed{ \ cos \ A = \frac{AD}{AB} \ }[/tex]
[tex]\boxed{ \ cos \ 60^0 = \frac{AD}{12} \ }[/tex]
[tex]\boxed{ \ \frac{1}{2} = \frac{AD}{12} \ }[/tex]
[tex]\boxed{ \ AD = 12 \times \frac{1}{2} \ }[/tex]
We get the length of AD is 6 cm.
Note:
[tex]\boxed{ \ sin \theta = \frac{opposite}{hypotenuse} \ } \ \boxed{ \ S = O / H \ }[/tex]
[tex]\boxed{ \ cos \theta = \frac{adjacent}{hypotenuse} \ } \ \boxed{ \ C = A / H \ }[/tex]
[tex]\boxed{ \ tan \theta = \frac{opposite}{adjacent} \ } \ \boxed{ \ T = O / A \ }[/tex]
[tex]\boxed{ \ sin \ 30^0 = cos \ 60^0 = \frac{1}{2} \ }[/tex]
[tex]\boxed{ \ sin \ 45^0 = cos \ 45^0 = \frac{1}{2} \sqrt{2} \ }[/tex]
[tex]\boxed{ \ sin \ 60^0 = cos \ 30^0 = \frac{1}{2} \sqrt{3} \ }[/tex]
[tex]\boxed{ \ tan \ 30^0 = \frac{1}{\sqrt{3}} = \frac{1}{3} \sqrt{3} \ }[/tex]
[tex]\boxed{ \ tan \ 45^0 = 1 \ }[/tex]
[tex]\boxed{ \ tan \ 60^0 = \sqrt{3} \ }[/tex]
Learn more
- Finding the value of sine of angle https://brainly.com/question/9610296
- Multiple choice about trigonometric ratios https://brainly.com/question/1445273
- Trigonometric identities https://brainly.com/question/1980819
Keywords: the length, side AD, right-angled, adjacent, hypotenuse, opposite, sin, cos, tan, sum of measures of angles in triangle are 180°, 30°, 60°
