Question

the post office is at the corner of first street and main street, which forms a right angle. First Street intersects with oak street to the north, and main street intersects with oak street to the east. the intersection of first street and oak street forms an x° angle, and tan x°= 7/5. car A drives on main street for 21 miles to arrive at oak street. how far will car B have to travel on first street to get to oak street? 15 miles 20 miles 25.4 miles 29.4 miles

Answer 1

Answer:

15 miles is the correct answer.

Step-by-step explanation:

It is given that Post office is at the intersection point of First Street and Main Street and forms a right angle.

Please refer to the attached image, let us suppose post office is at point P.

Intersection of Oak street and First street is towards North and

Intersection of Oak street and Main street is towards East

PQ represents the Main Street and PR represents the First Street.

$\angle PRQ = x^\circ$

$tan x^\circ = \dfrac{7}{5}$

It is given that Car A drives 21 miles on main street to reach oak street

$\Rightarrow PQ = 21 miles$

To find:

How far will car B have to travel on first street to get to oak street?

i.e. PR = ?

Solution:

By trigonometric rules we know that

$tan \theta = \dfrac{\text{Perpendicular}}{\text{Base}}$

Here $\theta\ is\ x$, perpendicular is PQ i.e. 21 miles and Base is PR

$tan x^\circ=\dfrac{7}{5} = \dfrac{21}{PR}\\\Rightarrow \dfrac{21}{PR}=\dfrac{7}{5}\\\Rightarrow PR = \dfrac{21 \times 5}{7}\\\Rightarrow PR = 15\ miles$

Hence, 15 miles is the correct answer.