Applying the sine ratio and the law of sines, the value of h in the diagram is: B. 3.2 yards.
What is the Sine Ratio?
Sine ratio for solving a right triangle is: sin ∅ = opp/hyp.
Let's find AT in triangle BAT using the given Law of Sines:
m∠BTA = 180 - (180 - 57) - 46 = 11°
AB = 1 yd
m∠ABT = 46°
Using the law of sines, we have:
sin(m∠ABT)/AT = sin(m∠BTA)/AB
Plug in the values
sin(46)/AT = sin(11)/1
AT = sin(46) × 1 / sin(11)
AT = 3.8 yards
Find h using the sine ratio:
∅ = 57°
Opposite = h
Hypotenuse = AT = 3.8 yards
Substitute
sin 57 = h/3.8
h = sin 57 × 3.8
h ≈ 3.2 yards.
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