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AlladinOne [14]
2 years ago
8

The angle of elevation to a nearby tree from a point on the ground is measured to be 66^{\circ} ∘ . How tall is the tree if the

point on the ground is 68 feet from the tree? Round your answer to the nearest tenth of a foot if necessary.
Mathematics
1 answer:
Nimfa-mama [501]2 years ago
6 0

By comparing with a right triangle, we will see that the height of the tree is 62.12ft

<h3>How tall is the tree?</h3>

We can compare the situation with a right triangle. Such that the hypotenuse measures 68 ft, and an angle measures 66°.

We want to get the height of the tree, which would be the opposite cathetus, then we can use the relation:

Sin(a) = (opposite cathetus)/hypotenuse.

Sin(66°) = H/68ft

Tan(66°)*68ft = H = 62.12ft

The height of the tree is 62.12ft

If you want to learn more about right triangles, you can read:

brainly.com/question/2217700

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A, B, C and D are four towns.
djverab [1.8K]

Three of the four towns are on the vertices of the triangle ΔCBD, through

which the bearing can calculated.

<h3>Response:</h3>
  • The bearing of D from B is approximately <u>209.05°</u>

<h3>Method by which the bearing is found;</h3>

From the given information, we have;

AC = AB = 25 km

∠BAC = 90° (definition of angle between north and east)

ΔABC = An isosceles right triangle (definition)

∠ACD = ∠ABC = 45° (base angles of an isosceles right triangle)

tan(\angle ABD) = \dfrac{45}{25}

  • \angle ABD = arctan \left(\dfrac{45}{25} \right)  \approx 60.945^{\circ}

The bearing of <em>D</em> from <em>B</em> is the angle measured from the north of <em>B</em> to the

direction of <em>D.</em>

<em />

Therefore;

  • The bearing of D from B ≈ 90° + (180° - 60.945°) = <u>209.05°</u>

Learn more about bearings in mathematics here:

brainly.com/question/10710413

5 0
3 years ago
In ΔWXY, x = 680 inches, w = 900 inches and ∠W=157°. Find all possible values of ∠X, to the nearest degree.
ikadub [295]

Given:

In ΔWXY, x = 680 inches, w = 900 inches and ∠W=157°.

To find:

The all possible values of ∠X, to the nearest degree.

Solution:

Law of Sines:

\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}

For ΔWXY,

\dfrac{w}{\sin W}=\dfrac{x}{\sin X}=\dfrac{y}{\sin Y}

Now,

\dfrac{w}{\sin W}=\dfrac{x}{\sin X}

\dfrac{900}{\sin (157^\circ)}=\dfrac{680}{\sin X}

900\sin X=680\sin (157^\circ)

\sin X=\dfrac{680}{900}\sin (157^\circ)

\sin X=0.295219

X=\sin^{-1}(0.295219)

X=17.17067

X\approx 17

Therefore, the value of ∠X is 17 degrees.

5 0
3 years ago
Y = 3x - 4<br> y = 4 + x
Andrei [34K]
Is This Substitution?

Cause if it is, then Y = 3x - 4
                              Y = 4 + x
= (4, 8)
7 0
3 years ago
A step function h(x) is represented by y = -2Lx] Which phrase best describes the range of the function h(x)?
Pani-rosa [81]

The phrase best describes the range of the function h(x) is option A: all real numbers.

<h3>What is a range of a function?</h3>

The range is the set of all values which the given function can output.

A step function h(x) is represented by y = -2|x|.

The mode of x gives the real number every time by putting the values.

The phrase best describes the range of the function h(x) is option A: all real numbers.

Learn more about appropriate domain and range here:

brainly.com/question/20073127

#SPJ1

5 0
2 years ago
Keith weighs 20 kg more than Beth,while henry weighs 30kg less than twice as much as Beth. If Keith and Henry weigh the same, ho
dybincka [34]

Answer:

50kg

Step-by-step explanation:

K = Keith  B = Beth  H = Henry

K = 20 + B

H = 2B - 30

K = H

20 + B = 2B - 30

B = 50kg

3 0
3 years ago
Read 2 more answers
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