Question

Question 72 true or false

Answer 1

True

m∠T = 40.4°

Explanation:

We know all the sides of the triangle but we do not know any of its angles.

To find out if the angle T = 40.4 ° we use the cosine theorem.

According to the cosine theorem:

`c^2=a^2 +b^2-2abcos(\alpha)`

Where
`\alpha` is the angle between a and b.

In this case:

`\alpha = T\\\\a= 11\\\\b=13\\\\c= 8.5`

Then we clear α from the formula and verify that it is equal to 40.4 °

`8.5^2 =11^2 + 13^2 -2(11)(13)cos(\alpha)\\\\8.5^2 -11^2 - 13^2= -2(11)(13)cos(\alpha)\\\\-8.5^2 +11^2 + 13^2= 2(11)(13)cos(\alpha)\\\\(-8.5^2 +11^2 + 13^2)/(2(11)(13))=cos(\alpha)\\\\\alpha=arcos((-8.5^2 +11^2 + 13^2)/(2(11)(13)))\\\\\alpha = 40.4\° =T`