Question

A pole tilts toward the sun at a 12° angle from the vertical, and it casts a 20-foot shadow. The angle of elevation from the tip of the shadow to the top of the pole is 36°. What is the length of the pole? Round your answer to the nearest tenth.
A) 4.5 ft
B) 7.1 ft
C) 11.8 ft
D) 17.6 ft

Answer 1

The length of the pole is $\boxed{17.6{\text{ feet}}}$. Option (D) is correct.

Further explanation:

The Pythagorean formula can be expressed as,

$\boxed{{H^2} = {P^2} + {B^2}}.$

Here, H represents the hypotenuse, P represents the perpendicular and B represents the base.

The formula for tan of angle a can be expressed as

$\boxed{\tan a = \frac{P}{B}}$

Given:

The options are as follows,

(A). $4.5{\text{ feet}}$

(B). $7.1{\text{ feet}}$

(C). $11.8{\text{ feet}}$

(D). $17.6{\text{ feet}}$

Explanation:

A pole tilts toward the sun at a ${12^ \circ }$ angle from the vertical, and it casts a 20-foot shadow.

The angle of elevation from the tip of the shadow to the top of the pole is ${36^ \circ }.$

In triangle ABC,

$\begin{aligned}\tan {36^ \circ }&= \frac{{AB}}{{BC}}\\0.727&= \frac{{AB}}{{20}}\\20 \times 0.727&= AB\\\end{aligned}$

The sum of all angles of triangle is ${180^ \circ }.$

$\begin{aligned}\angle BDC + \angle DCB + \angle CBD &= {180^ \circ }\\\angle BDC + 36 + \left( {90 + 12} \right) &= {180^ \circ }\\\angle BDC + 148 &= {180^ \circ } \\\angle BDC &= {180^ \circ } - {148^ \circ }\\\angle BDC &= {42^ \circ } \\\end{aligned}$

Use sine law in triangle ABC.

$\begin{aligned}\frac{{BC}}{{\sin D}} &= \frac{{BD}}{{\sin C}}\\\frac{{20}}{{\sin 42}} &= \frac{{BD}}{{\sin 36}} \\ \frac{{20}}{{\sin 42}} \times \sin 36 &= BD\\\frac{{20}}{{0.669}} \times 0.588 &= BD\\17.6&= BD\\\end{aligned}$

The length of the pole is $\boxed{17.6{\text{ feet}}}$. Option (D) is correct.

Learn more:

1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.
2. Learn more about equation of circle brainly.com/question/1506955.
3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Trigonometry

Keywords: Pole, tilts, sun, 12 degree angle, vertical, casts, 200-foot, shadow, top, pole, 36 degree, length, length of pole, nearest tenth, 4.5 feet, 7.1 feet, 11.8 feet, 17.6 feet.

Answer 2

ANSWER IS D.

Process:

See in the attached fig,

BD=length of pole=?

AB=length of vertical(imagine)

BC=length of shadow=20 ft

In traingle ABC,

tan(36)=AB/BC

AB=tan(36)*20

AB=14.5308 ft

Now we find <BDC to use sine law.

For that,

<BDC+<DCB+<CBD=180

<BDC+36+(90+12)=180

<BDC=180-112-36

<BDC=42

Now we use sine law in traingle ABC,

BC/sin (<BDC) =BD/sin (<DCB)

20/sin(42)=BD/sin(36)

BD=(20*sin36)/sin42

BD=17.56=17.6(approx) >>>>>>>>ANSWER D