Question

Given right triangle ABC with altitude BD drawn to hypotenuse AC. If AD = 5

ind AC = 13, what is the length of AB in simplest radical form? (Note: the figure
is not drawn to scale.)

Answer 1

8.06

Explanation:

We can find the length of AB using the principle of similar triangles on the triangles ABD and ABC. We would also engage the use of trigonometrical ratios which may be expressed in the form SOA CAH TOA Where,

SOA stands for

Sin Ф = opposite side/hypotenuses side

Cosine Ф = adjacent side/hypotenuses side

Tangent Ф = opposite side/adjacent side

Considering triangle ABD, given that AD = 5 then

Cos A = AD/AB

Also,

Cos A = AB/AC

Given that AD = 5, AC = 13, AB = x

therefore,

x/13 = 5/x

x² = 65

x = √65

= 8.06