Question

A blimp can be seen flying at an altitude of 5500 feet above a motor speedway during a race. The slanted distance directly to the pagoda at the startdashfinish line is d feet. Express the horizontal distance h as a function of d.

Answer 1

Answer:

The expression of h as function of x is   h = $\sqrt{(d + 5500) (d - 5500)}$

Step-by-step explanation:

Given as :

The distance of blimp  (AB) = 5500 feet

The slanted distance to the pagoda (BC) = d feet

The horizontal distance (AC) = h

Let the angle made between slanted distance and horizontal distance be Ф

So , cos Ф = $\frac{AC}{BC}$ = $\frac{h}{d}$

And sin Ф =  $\frac{AB}{BC}$ = $\frac{5500}{d}$

∵, cos²Ф = 1 - sin²Ф

So, $(\frac{h}{d})^{2}$ = $1 - (\frac{5500}{d})^{2}$

Or, $(\frac{h}{d})^{2}$ = $(\frac{d^{2}- 5500^{2}}{d^{2}})$

Or,                                     h² = d² - 5500²

∴                                        h = $\sqrt{d^{2}- 5500^{2}}$

Or,                                     h = $\sqrt{(d + 5500) (d - 5500)}$

Hence The expression of h as function of x is   h = $\sqrt{(d + 5500) (d - 5500)}$     Answer