In δabc, m∠cab = 60° and ad is angle bisector with d∈ bc and ad = 8 ft. find the distances from d to the sides of the triangle.

4 ft.

Step-by-step explanation:

Given: In ΔABC, m∠CAB = 60° and AD is angle bisector with D∈ BC and AD = 8 ft.

Draw a diagram according to the given information, the draw altitude on each side from point D.

We need to find the length of the altitude.

AD is an angle bisector, So, AD divides the angle m∠CAB = 60° in two equal parts.

In a right angle triangle,

In triangle ADE,

Multiply both sides by 8.

Therefore, the value of DE is 4 ft.

In triangle ADE and ADF,

            (AD is angle bisector)

            (Right angles)

                               (Reflexive property)

By AAS triangle ADE and ADF are congruent. The corresponding parts of congruent triangles are congruent.

Therefore, the distances from D to the sides of the triangle is 4 ft.

34.5 cm

step-by-step explanation:

generally for a circular segment of angle, θ° and radius r

arc length

= (θ/360) x circumference

= (θ/360) x 2πr

in our case, θ = 60°, π=3.142 and r = 33 cm

substitute into above formula

arc length

= (60/360) x 2(3.142)( 33) = 34.5 cm