Question

In the following diagram increment A B C comma space increment A C D comma space increment A D E comma space increment A E F comma space a n d space increment A F G are all right triangles. If BC = 3 , find the length of top enclose A G end enclose .

Answer 1

The length AG is 10.67.

How the length of AG is computed.

From the the given figure

Since all the triangles are right triangle

From ∆ABC

Measure of ∠B = 90⁰

sin30 = 3/AC

AC = 3/sin30

= 3/0.5 = 6

In ∆ACD

cos30 = AC/AD

AD = 6/cos30

AD = 12/√3

= 4√3

In ∆ADE

cos30 = AD/AE

co30 = 4√3/AE

AE = 4√3/cos30

= 8√3/√3

= 8

In ∆AEF

cos30 = 8/FA

= 8/cos30

FA = 16/√3

In ∆AFG

cos30 = (16/√3)/x

AG = (16/√3)/√3/2

= 16/√3 * 2/√3

= 32/3

= 10.67

length AG is 10.67.

Complete question