Question

The two triangles shown in the figure are similar. Find the distance, d, across Coyote Ravine.

Answer 1

We can see that both triangles are right angle triangle as per information given into picture. So we will prove that they are similar then use properties of similar triangle to find the value of d.

In triangle STV and triangle XWV:

∠STV = ∠XWV { both are equal to 90 degree}

∠TVS = ∠WVX { vertically opposite angles are equal}

Hence by AA (Angle Angle) similarity postulate of the triangles, It is proved that triangle STV and triangle XWV are similar.

We know that ratio of corresponding sides of similar triangles are equal so we can write:

$\frac{ST}{XW}=\frac{TV}{WV}$

$\frac{350}{d}=\frac{400}{180}$

350*180=400d

63000=400d

divide both side by 400

157.5=d

Hence final answer is d=157.5  m.