Question

if ABC if a =13 b=14c=15 find tha value of cos ​

Answer 1

Step-by-step explanation:

Here we have our 13–14–15 triangle.

First of all, we must find cos(A)

Using the cosine law:

BC2=AB2+AC2−2∗AB∗AC∗cos(A)

142=132+152−2∗13∗15∗cos(A)

196=169+225−390∗cos(A)

198=390∗cos(A)

⇒cos(A)=198390

cos(A)=3365

Next, we’ll find sin(A)

Using the Pythagorean Identity:

sin2(A)+cos2(A)=1

⇒sin(A)=1−cos2(A)−−−−−−−−−√

sin(A)=1−(3365)2−−−−−−−−√

sin(A)=1−10894225−−−−−−−√

sin(A)=31364225−−−−√

sin(A)=5665

Finally, we’ll use the half-angle formula:

sin(A2)=1−cos(A)2−−−−−−√

sin(A2)=1−56652−−−−√

sin(A2)=65−562∗65−−−−−√

sin(A2)=9130−−−√

Thus: sin(A2)=9130−−−√

Note: it can also be written as: sin(A2)=3130√130

Answer 2

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