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3 years ago

A tree 10 meters high casts a 17.3 meter shadow.

Mathematics

1 answer:

sashaice [31]3 years ago

5 0

Answer:

the angle of elevation of the sun is $\approx 30^o$

Step-by-step explanation:

Let's make a diagram of the tree, ground and inclination of the rays of the sun, so we understand what right angle triangle we have. Please see the attached image.

Notice that our unknown is the angle $\theta$ , and that we know the size of the side opposite to it, and of the side adjacent to it. Therefore the most convenient trigonometric formula to use is the tangent of the angle because:

$tan(\theta)=\frac{opposite}{adjacent} \\tan(\theta)=\frac{10}{17.3}\\\theta=arctan(\frac{10}{17.3})\\\theta\approx 30^o$

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Determine the 16th term of the sequence<br><br>9, 18, 36....<br><br>r________?

raketka [301]

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4 0

3 years ago

Find the value of a. A: 15, B: 19

loris [4]

Answer:

A: 15

Step-by-step explanation:

The angles are opposite to each other.

Vertically opposite angles are equal in size.

Put up an equation and solve for a.

6a + 10 = 3a + 55

Subtract 3a and 10 on both sides.

6a - 3a = 55 - 10

Combining like terms.

3a = 45

Divide both sides by 3.

a = 45/3

a = 15

The value of a is 15.

7 0

3 years ago

Read 2 more answers

Please help! Asap. Parent in need of explanation of math problem?

kotykmax [81]

The drawing shows that angles BAD and CAD are congruent, which means that the line segment AD bisects the angle BAC. By the angle bisector theorem,

$\dfrac{CD}{BD}=\dfrac{AC}{AB}$

But AB and AC are also shown to be congruent, so the right hand side reduces to 1, and we have $CD=BD$ , which means CD and BD are also congruent.

AD is congruent to itself and happens to be a part of two triangles, ABD and ACD.

So by the side-side-side postulate, the triangles ABD and ACD are congruent, which means corresponding parts (sides and angles) are congruent to each other. And because triangles ABD and ACD are congruent, the "total" triangle ABC is isosceles, and AD must be perpendicular to BC. This last observation means that $x=90$ .