Given that an intercepted arc has length 6pi inches and a central angle is pi/3, find the radius
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By applying the knowledge of similar triangles, the lengths of AE and AB are:
a.
b.
<em>See the image in the attachment for the referred diagram.</em>
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- The two triangles, triangle AEC and triangle BDC are similar triangles.
- Therefore, the ratio of the corresponding sides of triangles AEC and BDC will be the same.
<em>This implies that</em>:
- AC/BC = EC/DC = AE/DB
<em><u>Given:</u></em>
<u>a. </u><u>Find the length of </u><u>AE</u><u>:</u>
EC/DC = AE/DB
- Plug in the values
- Cross multiply
- Divide both sides by 5.4
<u>b. </u><u>Find the length of </u><u>AB:</u>
AC = 6.15 cm
To find BC, use AC/BC = EC/DC.
- Plug in the values
- Cross multiply
- Thus:
- Substitute
Therefore, by applying the knowledge of similar triangles, the lengths of AE and AB are:
a.
b.
Learn more here:
The hypotenuse of the triangle is given by:
Substituting values:
Clearing CB we have:
Then, the perimeter of the triangle is:
Substituting values:
Answer:
the perimeter of triangle BRC in units is:
D.6 + 2√5
Substituting values:
Clearing CB we have:
Then, the perimeter of the triangle is:
Substituting values:
Answer:
the perimeter of triangle BRC in units is:
D.6 + 2√5