Question

Can you please help me

Answer 1

Answer:

p = 4.0

q = 2.0

angle <P = 64 degrees

Step-by-step 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:

$cos(26^o)= \frac{adjacent}{hypotenuse} \\cos(26^o)= \frac{p}{4.5}\\p= 4.5 *cos(26^o)\\p=4.0445$

which rounded to the nearest tenth gives :  p = 4.0

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

$sin(26^o)= \frac{opposite}{hypotenuse} \\sin(26^o)= \frac{q}{4.5}\\q= 4.5 *sin(26^o)\\q=1.9726$

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