Question

Given △PQR ~ △STU, find the missing measures in △STU. Triangles P Q R and S T U. Side P Q has length 14, side Q R has length 28, and side R P has length 21. Angle P has measure 70 degrees and angle R has measure 46 degrees. In triangle S T U, side U S has length 6. No other measures are given. SU ST TU m∠S m∠T m∠U 6

Answer 1

The missing measures in triangle STU are:

SU = 14, ST = (2/3)TU, TU = (4/3)ST, m∠S = 70 degrees, m∠T = 64 degrees, m∠U = 46 degrees.

Explanation:

Since triangles PQR and STU are similar, their corresponding sides are in proportion, and their corresponding angles are congruent. We can use this information to find the missing measures in triangle STU:

Since side PQ corresponds to side ST, we have:

ST/PQ = TU/PR

Substituting the given values, we get:

ST/14 = TU/21

Cross-multiplying, we get:

ST × 21 = 14 × TU

ST = (14/21)TU

Simplifying, we get:

ST = (2/3)TU

Since side QR corresponds to side TU, we have:

TU/QR = ST/RP

Substituting the given values, we get:

TU/28 = ST/21

Cross-multiplying, we get:

TU × 21 = 28 × ST

TU = (28/21)ST

Simplifying, we get:

TU = (4/3)ST

Since angle P corresponds to angle S, we have:

m∠S = m∠P = 70 degrees

Since angle R corresponds to angle U, we have:

m∠U = m∠R = 46 degrees

To find m∠T, we can use the fact that the angles in a triangle add up to 180 degrees:

m∠S + m∠T + m∠U = 180

Substituting the given values, we get:

70 + m∠T + 46 = 180

Simplifying, we get:

m∠T = 64 degrees

To find SU, we can use the fact that the corresponding sides are in proportion:

SU/PR = ST/PQ

Substituting the given values, we get:

SU/21 = (2/3)

Cross-multiplying, we get:

SU = 14

Therefore, the missing measures in triangle STU are:

SU = 14

ST = (2/3)TU

TU = (4/3)ST

m∠S = 70 degrees

m∠T = 64 degrees

m∠U = 46 degrees.

Hope this helps! Sorry if it doesn't. If you need more help, ask me! :]