Answer:
a) angle QRP is 92 degrees, side QR is 23 cm, angle RPQ is 47 degrees
b) angle EFD is 65 degrees, side FD is 22cm, side ED is 20cm
Step-by-step explanation:
a) in the first example, you know that u are given QR, PR, and angle PRQ, and u are asked to find triangle PQR,or the rest of the lengths.
step 1-u draw an example of the triangle, i will provide one for each at the bottom of this answer
step 2-lets find the sides first with the pythagorean theorem, which will mean 25²+x²=34². Pythagorean theorem is a²+b²=c²
step 3-after solving for x, x will be 23.04, which means the third side is 23 cm (after rounding).
step 4-now that we have all the sides, we can solve for the rest of the angles, by trigonometric ratios, we are gonna use sine for angle RPQ, sine is sin(the angle u want to find)=opposite side/hypotenuse.
step 5- so sin(RPQ)=25/34, and solve for RPQ on a calculator (i used math) and angle RPQ will equal 47.3 degrees.
step 6- just subtract the sum of both angles from 180 an the last angle will be 92 degrees.
b) u are given the measure of angles FED and EDF and the side length FE, we will solve for the last angle first then we will go for the side engths
step 1- we subtract the sum of the two angles we have from 180 and we will get the measure of angle EFD to be 65 degrees, now we have the angles and we want to find he sides.
step 2-we use sine of angle 31 degrees to find the hypotenuse, but it is opposite of sine since we want to find the side, not the angle, so we will use sin(31)=11.3/x, the sine equation is written like sin(the angle u have)=opposite/hypotenuse.
step 3- after solving for arc sine in a calculator, u will find side FD to be 22cm, and now to find the last side.
step 4-i will use the sine of angle 65 degrees to solve for side ED, it will be sin(65)=x/22, which will make side ED equal 20 cm in length.
ur welcome :)
hope i helped
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