Ans: Four shortcuts allow students to know two triangles must be congruent: SSS, SAS, ASA, and AAS. Knowing only side-side-angle (SSA) does not work because the unknown side could be located in two different places. The same is true for side angle side, angle side angle and angle angle side.
If the given pairs are supposed to represent points on the graph, you apparently have a graph in which y is inversely related to x. The constant of variation is the product of x and y values: 24. (matches selection B.)
A) cos θ = -(√24)/7 and tan θ = 5/√24 and
B) sec θ = 7/(√24) and tan θ = -5/(√24)
Sine is the ratio of the opposite side of an angle to the hypotenuse. Since sin θ = -5/7, the opposite side is -5 and the hypotenuse is 7.
For A, if the cosine is -√24/7, and the sine was -5/7, then the opposite/adjacent, tangent, would be -5/-(√24). However, two negatives divided make a positive, so the tangent would be 5/√24.
For B: the secant is 1/cos. This means it is the reciprocal, or flip, of the cosine. Instead of A/H, sec = H/A. This means the hypotenuse is 7 and the adjacent side is √24. Tangent = opposite/adjacent; this gives us -5/√24.
For C: the secant, H/A, is -7/5. This means the tangent, O/A, would be -5/5 = -1. This is incorrect.
For D: the cosine, A/H, is √24/7. This means the tangent, O/A, would be -5/√24; this is incorrect.
