How to I find a? It’s round to the nearest tenth.
1 answer:
Answer:
a ≈ 21.8
Step-by-step explanation:
We require the third angle in the triangle
Subtract the sum of the 2 angles from 180
third angle = 180° - (75 + 31.8)° = 180° - 106.8° = 73.2°
Using the Sine rule, that is
=
( cross- multiply )
a × sin75° = 22 × sin73.2° ( divide both sides by sin75° )
a = ≈ 21.8 ( to the nearest tenth )
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Answer:
Step-by-step explanation:
Hello there!
The first thing we want to do is find the measure of the large leg
To do so we use the Pythagorean theorem which says
where a and b are legs and c is the hypotenuse
we want to find b given the hypotenuse and short leg
so
all we have to do is plug in a ( a = short leg so a would equal 12) and c ( c = hypotenuse so c would equal 37)
so
so the longer leg is equal to 35
35=5x
divide each side by 5
5x/5=x
35/5=7
we're left with x=7
Option A: The height of the cylinder is equal to the diameter of the sphere.
Option C: The radius of the sphere is half the height of the cylinder.
Option E: The volume of the sphere is two-thirds the volume of the cylinder.
Solution:
The sphere is inside the cylinder.
Let r be the radius of the sphere.
Option A: The height of the cylinder is equal to the diameter of the sphere.
The sphere is fully occupied the cylinder.
If we draw the vertical line through enter of the sphere, which is equal to the height of cylinder.That is h = d. It is true.
Option B: The height of the cylinder is two times the diameter of the sphere.
That is h = 2d. From the above option, we know that h = d.
So, it is not true.
Option C: The radius of the sphere is half the height of the cylinder.
we know that diameter = 2 × radius (d = 2r)
From option A, we have h = d.
Substitute d = 2r, we get
⇒ h = 2r
Divide by 2 on both sides, we get
Therefore, it is true.
Option D: The diameter of the sphere is equal to the radius of the cylinder.
It is not true, because diameters of both cylinder and sphere are equal.
Option E: The volume of the sphere is two-thirds the volume of the cylinder.
Radius of cylinder and sphere = r
Height of cylinder h = 2r (by option C)
Volume of cylinder = Volume of sphere
(formula)
Hence it is true.
Option A, option C and option E are true.