Question

Seorang anak dengan tinggi 160 cm berdiri di depan menara dan melihat puncak menara dengan sudut elevasi 30 derajat,ia lalu berjalan sejauh 20 m mendekati menara dengan sudut elevasi 60 derajat .tinggi menara tersebut

Answer 1

d - the distance from the child to the tower;
h  - the height of the tower ( h = x + 1.6 m )
The system is:
tan 30° = x / d
tan 60° = x / ( d - 20 )
-------------------------------
the 1st equation:    1 / √3  = x / d        ⇒   d = x √3
the 2nd equation:    √3 = x / ( d - 20 )
-------------------------------------------------
√3 = x / ( x √3 - 20 )     / · ( x√3 - 20 )         ( we will multiple both sides )
√3 ( x √3 - 20 ) = x
3 x - 20 √3 = x
3 x - x = 20 √3
2 x = 20 √3
x = 20 √3  : 2
x = 10 √ 3 ≈  17.3 m
The height of the tower ( menara ):
h = 10 √ 3 + 1.6 m ≈ 17.3 + 1.6 ≈ 18.9 m 

Answer 2

The height of the tower is $\boxed{18.92{\text{ m}}}.$

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

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

Explanation:

In triangle ABF,

$\begin{aligned}\tan {60^ \circ }&= \frac{H}{x}\\\sqrt3&= \frac{H}{x}\\\sqrt 3 x &= H\\\end{aligned}$

In triangle ABE,

$\begin{aligned}\tan{30^ \circ }&= \frac{H}{{20 + x}}\\\frac{1}{{\sqrt3 }}&= \frac{H}{{20 + x}}\\\sqrt 3 H&= 20 + x\\H&=\frac{{20 + x}}{{\sqrt 3 }}\\\end{aligned}$

Equate the value of H.

$\begin{aligned}\sqrt 3 x &= \frac{{20 + x}}{{\sqrt 3 }}\\\sqrt 3 x \times \sqrt3 & = 20 + x \\3x &= 20 + x\\ 3x - x &= 20 \\ 2x &= 20\\x&=10 \\\end{aligned}$

The value of H can be obtained as follows,

$\begin{aligned}H&= \sqrt3\times 10\\&= 10 \times 1.732\\&= 17.32\\\end{aligned}$

The height of the tower can be obtained as follows,

$\begin{aligned}h&= H + 1.60\\&= 17.32 + 1.60 \\ &= 18.92\\\end{aligned}$

The height of the tower is $\boxed{18.92{\text{ m}}}.$

Kindly refer to the image attached.

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 https://brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Trigonometry

Keywords: tower, a child, height of 160 cm, elevation angle, 30 degree, 60 degree, he walks, far, approaching tower, elevation, height of tower.