n this triangle, what is the value of x? Enter your answer, rounded to the nearest tenth, in the box. x = cm A right triangle wi
th one leg labeled x and the hypotenuse labeled 85 centimeters. The angle that is opposite the leg labeled x centimeters is labeled 63 degrees.
2 answers:
See the attached picture to better understand the problem
we know that
in the right triangle ABC
sin 63°=AB/BC
AB is the opposite side angle 63-----> x cm
BC is the hypotenuse-----> 85 cm
AB=BC*sin 63°-----> AB=85*sin 63-----> AB=75.736 cm
AB=75.8 cm
the answer is
the value of x is 75.8 cm
we know that
in the right triangle ABC
sin 63°=AB/BC
AB is the opposite side angle 63-----> x cm
BC is the hypotenuse-----> 85 cm
AB=BC*sin 63°-----> AB=85*sin 63-----> AB=75.736 cm
AB=75.8 cm
the answer is
the value of x is 75.8 cm
Answer:
75.7 meters.
Step-by-step explanation:
Please find the attachment.
We have been given that a right triangle with one leg labeled x and the hypotenuse labeled 85 centimeters. The angle that is opposite the leg labeled x centimeters is labeled 63 degrees.
To find the value of x we will use sine as sine relates the opposite side of a right triangle to hypotenuse.
Upon substituting our given values in above formula we will get,
Therefore, the value of x is 75.7 to the nearest tenth.
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Answer:
Exact height = 8*sqrt(3) mm
Approximate height = 13.856 mm
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Explanation:
If you do a vertical cross section of the cylinder, then the 3D shape will flatten into a rectangle as shown in the diagram below.
After flattening the picture, I've added the points A through F
- point A is the center of the sphere and cylinder
- points B through E are the corner points where the cylinder touches the sphere
- point F is at the same horizontal level as point A, and it's on the edge of the cylinder.
Those point labels will help solve the problem. We're told that the radius of the sphere is 8 mm. So that means segment AD = 8 mm.
Also, we know that FA = 4 mm because this is the radius of the cylinder.
Focus on triangle AFD. We need to find the height x (aka segment FD) of this triangle so we can then double it later to find the height of the cylinder. This in turn will determine the height of the bead.
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As the hint suggests, we'll use the pythagorean theorem
a^2 + b^2 = c^2
b = sqrt(c^2 - a^2)
x = sqrt(8^2 - 4^2)
x = sqrt(48)
x = sqrt(16*3)
x = sqrt(16)*sqrt(3)
x = 4*sqrt(3)
This is the distance from D to F
The distance from D to E is twice that value, so DE = 2*(FD) = 2*4*sqrt(3) = 8*sqrt(3) is the exact height of the bead (since it's the exact height of the cylinder).
Side note: 8*sqrt(3) = 13.856 approximately.
