Question

cm and _BAC
AC = 6 cm, AB = 5
In the adjacent figure,
30°. Find the area of
the triangle​

Answer 1

Step-by-step explanation:

Step 1: Recall the area formula of the triangle and note down the important points

GIVEN: Triangle ABC

AB = 5 cm

AC = 6 cm

\angle BAC = 30\degree∠BAC=30°

FORMULA: Area of the triangle = 1/2 × b ×h

Step 2: Construct a perpendicular line to AC through B to base AC

Step 3: Calculate the height of the triangle

NOTE: \sin \theta = \frac{opposite}{hypotenuse}sinθ=

hypotenuse

opposite

\sin 30\degree = \frac{BD}{AB}sin30°=

AB

BD

\frac{1}{2} = \frac{BD}{5}

2

1

=

5

BD

BD = \frac{5}{2}BD=

2

5

Height BD = 2.5 cm

Step 4: Find the area of the triangle

Area of the triangle = \frac{1}{2} AC*BD

2

1

AC∗BD

= \frac{1}{2} 6 * 2.5

2

1

6∗2.5

= 3 * 2.5

= 7.5 cm^2 cm

2

Area of the triangle = 7.5