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Sever21 [200]
3 years ago
7

-2.25 as a fraction

Mathematics
1 answer:
denis-greek [22]3 years ago
5 0
- 2 1/4 (mix fraction)
- 9/4 (improper fraction)
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In right △ABC, the altitude CH to the hypotenuse AB intersects angle bisector AL in point D. Find the sides of △ABC if AD = 8 cm
tangare [24]

Answer:

AC=8\sqrt{3}\ cm\\ \\AB=16\sqrt{3}\ cm\\ \\BC=24\ cm

Step-by-step explanation:

Consider right triangle ADH ( it is right triangle, because CH is the altitude). In this triangle, the hypotenuse AD = 8 cm and the leg DH = 4 cm. If the leg is half of the hypotenuse, then the opposite to this leg angle is equal to 30°.

By the Pythagorean theorem,

AD^2=AH^2+DH^2\\ \\8^2=AH^2+4^2\\ \\AH^2=64-16=48\\ \\AH=\sqrt{48}=4\sqrt{3}\ cm

AL is angle A bisector, then angle A is 60°. Use the angle's bisector property:

\dfrac{CA}{CD}=\dfrac{AH}{HD}\\ \\\dfrac{CA}{CD}=\dfrac{4\sqrt{3}}{4}=\sqrt{3}\Rightarrow CA=\sqrt{3}CD

Consider right triangle CAH.By the Pythagorean theorem,

CA^2=CH^2+AH^2\\ \\(\sqrt{3}CD)^2=(CD+4)^2+(4\sqrt{3})^2\\ \\3CD^2=CD^2+8CD+16+48\\ \\2CD^2-8CD-64=0\\ \\CD^2-4CD-32=0\\ \\D=(-4)^2-4\cdot 1\cdot (-32)=16+128=144\\ \\CD_{1,2}=\dfrac{-(-4)\pm\sqrt{144}}{2\cdot 1}=\dfrac{4\pm 12}{2}=-4,\ 8

The length cannot be negative, so CD=8 cm and

CA=\sqrt{3}CD=8\sqrt{3}\ cm

In right triangle ABC, angle B = 90° - 60° = 30°, leg AC is opposite to 30°, and the hypotenuse AB is twice the leg AC. Hence,

AB=2CA=16\sqrt{3}\ cm

By the Pythagorean theorem,

BC^2=AB^2-AC^2\\ \\BC^2=(16\sqrt{3})^2-(8\sqrt{3})^2=256\cdot 3-64\cdot 3=576\\ \\BC=24\ cm

3 0
2 years ago
2x^2 -19x + 35 =0<br> Factor
nignag [31]

Answer:

Step-by-step explanation:

3 0
3 years ago
It has rained 3/5 inch in 1/4 hour. If it continues to rain at the same rate,how much rain would fall in an hour
Scorpion4ik [409]

Answer:

2 2/5 inches

Step-by-step explanation:

3/5 x 4

3/5 x 4/1

3/5 x 4/1 = 12/5

12/5 = 2 2/5

5 0
3 years ago
How is trigonometry used to locate the position of a wildfire.
Dahasolnce [82]

Answer:

Sine Function sin Opposite side/ Hypotenuse

Tangent Function tan Opposite side / Adjacent side

Cosine Function cos Adjacent side / Hypotenuse

Cosecant Function cosec Hypotenuse / Opposite side

Step-by-step explanation:

Your welcome

5 0
3 years ago
What is the factored form of 6x^2 + 13x + 6?
LekaFEV [45]

Answer:

(3x+2)(2x+3)

Step-by-step explanation:

6x2+13x+6

6x2+13x+6

=(3x+2)(2x+3)

7 0
3 years ago
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