177k views
2 votes
Need help!

I’m the following right triangle PQR,find the missing side x, and R if angle Q=70 degrees.Also find the 6 T ratios

Need help! I’m the following right triangle PQR,find the missing side x, and R if-example-1
User Promzy
by
7.8k points

1 Answer

2 votes

Explanation:

first of all, there is the rule for all types of triangles : the sum of all angles in a triangle is always 180°.

and for right-angled triangles there is also Pythagoras :

c² = a² + b²

with c being the Hypotenuse (the side opposite of the 90° angle), and a, b being the legs.

so, with these rules we can get all missing elements :

180 = 90 + angle Q + angle R

180 = 90 + 70 + angle R

20° = angle R

30² = 24² + x²

900 = 576 + x²

324 = x²

x = sqrt(324) = 18

the 6 trigonometric ratios (functions) of any angle are

sine

cosine

tangent

cotangent

secant

cosecant

there is something very wrong with the numbers.

a triangle with the sides 30, 24, 18 cannot have the angles 90°, 70°, 20°.

the angles are with these sides

P = 90°

Q = 36.87°

R = 53.13°

or a triangle with the angles 90°, 70°, 20° and the Hypotenuse = 30 has the legs

PQ = 10.261

PR = 28.191

the given sides do not fit to the given angles.

I will give you now the trigonometric ratios of Q based on the calculated side lengths 30, 24, 18 and ignore the specified angle sizes :

sin(Q) = opposite/ Hypotenuse = 18/30 = 3/5 = 0.6

Q = 36.87°

cos(Q) = adjacent/ Hypotenuse = 24/30 = 4/5 = 0.8

Q = 36.87°

tan(Q) = opposite/ adjacent = sin(Q)/cos(Q) = 18/24 =

= 3/4 = 0.75 Q = 36.87°

cot(Q) = adjacent/ opposite = 24/18 = 4/3 = 1.33333...

Q = 36.87°

sec(Q) = Hypotenuse/ adjacent = 30/24 = 5/4 = 1.25

Q = 36.87°

csc(Q) = Hypotenuse/ opposite = 30/18 = 5/3 = 1.6666...

Q = 36.87°

if the sides of the right-angled triangle are truly 30, 24, 18, then Q = 36.87° (confirmed by all 6 trigonometric ratios), and above are all 6 trigonometric ratios for that angle.

User Ostad
by
8.6k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.