All categories

3 years ago

A tree casts a 12 foot shadow while the sun is at an angle of elevation of 58º. Use

Mathematics

1 answer:

Shkiper50 [21]3 years ago

3 0

The height of tree is 32 meter

Solution:

Given that, The sun is at an angle of elevation of 58 degree

A tree casts a shadow 20 meters long on the ground

The sun, tree and shadow forms a right angled triangle

The figure is attached below

ABC is a right angled triangle

AC is the height of tree

AB is the length of shadow

AB = 20 meters

Angle of elevation, angle B = 58 degree

By definition of tan,

$tan \theta = \frac{opposite}{adjacent}$

In this right angled triangle ABC,

opposite = AC and adjacent = AB

Therefore,

$tan\ 58 = \frac{AC}{AB}\\\\tan\ 58 = \frac{AC}{20}\\\\1.6 = \frac{AC}{20}\\\\AC = 1.6 \times 20\\\\AC = 32$

Thus height of tree is 32 meter

You might be interested in

A man is 25 years old. His mother is exactly three times his age. How old will the man’s mother be when he is 35 years old?

klio [65]

Answer:

Step-by-step explanation:

Note the mother is 3x his age when he is 25 years old. Multiply 3 with 25:

3 x 25 = 75

Ten years pass (35 - 25 = 10). Add 10 to 75:

75 + 10 = 85

When the man is 35 years old, his mother will be 85 years old.

4 0

3 years ago

Whats 1 added up to 1?

Finger [1]

4 dude lol just playin 2

5 0

2 years ago

What’s the solution to the system of equations

sesenic [268]

Answer:

The answer to the system of equations is 4, -4

5 0

2 years ago

Read 2 more answers

Does anyone know how to solve this

Fofino [41]

Here is the answer the app is called cymath btw

3 0

3 years ago

Can u help me ASAP. i need to know how to do it step by step

12345 [234]

Answer:

19

Step-by-step explanation:

$f(x) =4x^3-8x^2+ax+b$ has a factor $2x-1$ and

when divided by $x+2$ , remainder is 20.

To find:Remainder when divided by (x-1) ?

Solution:

$2x-1$ is a factor

$2x - 1 = 0 \Rightarrow x = \frac{1}{2}$ when we put this value of x to the function, it will become 0.

i.e.

$\Rightarrow f(\dfrac{1}{2}) =0 =4\times (\dfrac{1}2)^3-8(\dfrac{1}2)^2+\dfrac{a}{2}+b=0\\\Rightarrow \dfrac{1}{2}-2+\dfrac{a}{2}+b=0\\\Rightarrow 1-4+a+2b=0\\\Rightarrow a +2b=3 ......(1)$

Remainder is 20 when f(x) is divided by $x+2$

i.e.

$f(-2) =20$

$\Rightarrow f(-2) =20 =4\times (-2)^3-8(-2)^2-2a+b=20\\\Rightarrow -32-32-2a+b=20\\\Rightarrow -2a+b=84 ...... (2)$

Solving (1) and (2), Multiply equation (1) by 2 and adding to (2):

$5b=6+84\\\Rightarrow b = \dfrac{90}{5} = \bold{18}$

By equation (1):

$a+2(18) = 3\\\Rightarrow a = -33$

So, the equation becomes:

$f(x) =4x^3-8x^2-33x+18$

$\Rightarrow f(1) = 4(1) -8 (1) -33(1) +18 = \bold{19}$

So, when divided by (x-1), remainder will be 19.

4 0

3 years ago