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:
[tex]cos(26^o)= \frac{adjacent}{hypotenuse} \\cos(26^o)= \frac{p}{4.5}\\p= 4.5 *cos(26^o)\\p=4.0445[/tex]
which rounded to the nearest tenth gives : p = 4.0
Now we use the sine function to help us determine side q:
[tex]sin(26^o)= \frac{opposite}{hypotenuse} \\sin(26^o)= \frac{q}{4.5}\\q= 4.5 *sin(26^o)\\q=1.9726[/tex]
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
