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2 years ago

In ΔPQR, the measure of ∠R=90°, the measure of ∠P=26°, and PQ = 8.5 feet. Find the length of QR to the nearest tenth of a foot.

Mathematics

2 answers:

Vitek1552 [10]2 years ago

5 0

Answer:

3.7feet

Step-by-step explanations

Using the sin rule

A/sin a = B/sin b

Let A = PQ = 8.5feet

B = QR = x feet

a = R = 90°

b = P = 26°

Substitute the values into the Sin rule

8.5/sin90 = x/sin26

8.5×sin 26 = x × sin 90

8.5×0.4383 = x× 1

3.7255 = x

Hence the length of QR to the nearest tenth 3.7feet

Andreas93 [3]2 years ago

4 0

Answer:

3.7

Step-by-step explanation:

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A board is leaning against a vertical wall. One end of the board rests on the ground at a point eight feet from the wall. The ot

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Step-by-step explanation:

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3 years ago

I suck at math if you could help me with these questions that would be great

docker41 [41]

Answer:

Part 8) The triangles are not similar (see the explanation)

Part 12) The triangles are not similar (see the explanation)

Part 14) The area is increased by 125%

Part 15) $h=30\ ft$

Step-by-step explanation:

Part 8) we know that

If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

<em>Find the value of x in the larger triangle</em>

The sum of the interior angles in any triangle must be equal to 180 degrees

$64^o+85^o+x=180^o$

$149^o+x=180^o$

$x=180^o-149^o$

$x=31^o$

<em>Find the value of y in the smaller triangle</em>

The sum of the interior angles in any triangle must be equal to 180 degrees

$26^o+85^o+y=180^o$

$111^o+y=180^o$

$y=180^o-111^o$

$y=69^o$

The corresponding angles of both triangles are not congruent

therefore

The triangles are not similar

Part 12) we know that

If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

The measure of the interior angles of the triangle of the left are

88°

29° ----> by vertical angles

and

180°-(88°+29°)=63° ---> the sum of the interior angles in any triangle must be equal to 180 degrees

The measure of the interior angles of the triangle of the right are

180°-91°=89° ----> the sum of a exterior angle and a interior angle is equal to 180 degrees

29°

and

180°-(89°+29°)=62° ---> the sum of the interior angles in any triangle must be equal to 180 degrees

The corresponding angles of both triangles are not congruent

therefore

The triangles are not similar

Part 14) we know that

If two figures are similar then the ratio of its areas is equal to the scale factor squared

In this problem the scale factor is 1.5

Because

100%+50%=150%=150/100=1.5

The scale factor squared is $1.5^2=2.25$

That means that the new area is 2.25 times the original area

The area is increased by 125%

Part 15)

Let

h ----> the height of the pine

we know that

The height of the person divided by the length of his shadow is equal to the height of the pine tree divided by the length of its shadow

using proportion

$\frac{6}{3}=\frac{h}{15}$

solve for h

$2=\frac{h}{15}$

$h=2(15)=30\ ft$

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