Which of the following best completes the proof showing that ΔWXZ ~ ΔXYZ? triangles WXZ and XYZ that share side XZ with right angle XZW, WZ equals 16, XZ equals 12, and YZ equals 9

Since segment XZ is perpendicular to segment WY, angles WZX and XZY are both right angles and congruent. The proportion shows the corresponding sides are proportional, so the triangles are similar by the SAS Similarity Postulate.

16 over 12 equals 9 over 12
16 over 12 equals 12 over 9
12 over 12 equals 16 over 9
12 over 16 equals 16 over 9

Christina can paint 420 square feet in 105 minutes. which unit rate describes the scenario?

Cone w has a radius of 8 cm and a height of 5 cm. square pyramid x has the same base area and height as cone w. paul and manuel disagree on how the volumes of cone w and square pyramid x are related. examine their arguments. which statement explains whose argument is correct and why? paul manuel the volume of square pyramid x is equal to the volume of cone w. this can be proven by finding the base area and volume of cone w, along with the volume of square pyramid x. the base area of cone w is π(r2) = π(82) = 200.96 cm2. the volume of cone w is one third(area of base)(h) = one third third(200.96)(5) = 334.93 cm3. the volume of square pyramid x is one third(area of base)(h) = one third(200.96)(5) = 334.93 cm3. the volume of square pyramid x is three times the volume of cone w. this can be proven by finding the base area and volume of cone w, along with the volume of square pyramid x. the base area of cone w is π(r2) = π(82) = 200.96 cm2. the volume of cone w is one third(area of base)(h) = one third(200.96)(5) = 334.93 cm3. the volume of square pyramid x is (area of base)(h) = (200.96)(5) = 1,004.8 cm3. paul's argument is correct; manuel used the incorrect formula to find the volume of square pyramid x. paul's argument is correct; manuel used the incorrect base area to find the volume of square pyramid x. manuel's argument is correct; paul used the incorrect formula to find the volume of square pyramid x. manuel's argument is correct; paul used the incorrect base area to find the volume of square pyramid x.

Abird on top of a 200 ft bridge tower sees a man standing on the lower part of the bridge (which is 50 ft above the ground). the angle of depression from the bird is 26 ̊. how far is the man from the base of the bridge tower? with explanation and pictures .