Question

Can you please help me

Answer 1

p = 4.0

q = 2.0

angle <P = 64 degrees

Explanation:

We can use the definition of cosine to find the value of side p (the adjacent side to the 26 degree angle, via the formula:

`cos(26^o)= (adjacent)/(hypotenuse) \\cos(26^o)= (p)/(4.5)\\p= 4.5 *cos(26^o)\\p=4.0445`

which rounded to the nearest tenth gives : p = 4.0

Now we use the sine function to help us determine side q:

`sin(26^o)= (opposite)/(hypotenuse) \\sin(26^o)= (q)/(4.5)\\q= 4.5 *sin(26^o)\\q=1.9726`

which rounded to the nearest tenth gives:

q = 2.0

Finally, we determine the measure of angle P using the fact that the addition of all internal angles of a triangle must add to 180 degrees:

< P + < Q + < R = 180

< P + 26 + 90 = 180

< P = 180 - 26 - 90

< P = 64 degrees