Triangles A B C and T P Q are shown. Angles B C A and P Q T are congruent.

What additional information could be used to prove that the triangles are congruent using AAS or ASA? Select three options.

AngleB ≅ AngleP and BC ≅ PQ

AngleA ≅ AngleT and AC = TQ = 3.2cm

AngleA ≅ AngleT and AngleB ≅ AngleP

AngleA ≅ AngleT and BC ≅ PQ

AC = TQ = 3.2 cm and CB = QP = 2.2 cm

5+2x=a

asdasdsaadsaddsasds

the value of x is 9 ⇒ answer b

step-by-step explanation:

* we can solve this problem using cosine and sine rule

- in δ abc

∵ ab = 36 , bc = 28 , ac = 16

- lets find the measure of angle b using the cosine rule

∵ cos b = [ab² + bc² - ac²]/2(ab)(bc)

∴ cos b = [36² + 28² - 16²]/2(36)(28)

∴ cos b = 19/21

∴ m∠b = cos^-1(19/21) ≅ 25°

- lets find the measure of angle a using the sine rule

∵ sina/bc = sinb/ac = sinc/ab

∴ sina/28 = sin25°/16 ⇒ by using cross multiplication

∴ sina = 28 × sin25°/16

∴ sina = 0.7396

∴ m∠a = sin^-1(0.7396) ≅ 48°

- from the figure m∠abd = m∠dbc

∵ m∠abc = 25°

∴ m∠abd = 25°/2 = 12.5°

- in δabd

∵ m∠a = 48° , m∠abd = 12.5°

∵ the sum of the measures of the interior angles of any δ is 180°

∴ m∠adb = 180° - (48° + 12.5°) = 119.5°

∵ ab = 36

∵ ad = x

- use the sine rule to find x

∵ sin∠adb/ab = sin∠abd/x

∴ sin119.5°/36 = sin12.5°/x ⇒ by using cross multiplication

∴ x = 36 × sin12.5°/sin119.5° = 8.95 ≅ 9

* the value of x is 9

you estimate that the angle of elevation to the top of the 86th floor (the observatory) is 82 .the total height of the building is another 123 meters above the 86th floor.

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