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07 Applications of Trigonometry Free Online FlashCards

Study 07 Applications of Trigonometry with 12 free online flashcards. Review key terms, definitions, and concepts with this interactive flashcard deck.

12 cards
01
Front

What is the hypotenuse?

Back

The hypotenuse is the side opposite the right angle. Relative to an acute angle, the other sides are the opposite and adjacent sides.

02
Front

State the three primary right-triangle ratios.

Back
sin⁡θ=oppositehypotenuse,cos⁡θ=adjacenthypotenuse,tan⁡θ=oppositeadjacent.\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}},\quad \cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}},\quad \tan\theta=\frac{\text{opposite}}{\text{adjacent}}.
03
Front

A 50-foot distance has a 68∘68^\circ elevation angle. Find the height.

Back

Using tangent, h=50tan⁡68∘≈123.8h=50\tan68^\circ\approx123.8 feet from eye level to the top.

04
Front

A 120-foot tower has a 25∘25^\circ depression angle. Find the car’s distance.

Back

The horizontal distance is d=120tan⁡25∘≈257.4d=\frac{120}{\tan25^\circ}\approx257.4 feet.

05
Front

What is the Law of Sines?

Back
asin⁡A=bsin⁡B=csin⁡C.\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}.
06
Front

In a triangle with A=42∘A=42^\circ and B=68∘B=68^\circ, find CC.

Back

C=180∘−42∘−68∘=70∘C=180^\circ-42^\circ-68^\circ=70^\circ.

07
Front

What makes the SSA case ambiguous?

Back

SSA is ambiguous: depending on the measurements, it can produce zero, one, or two possible triangles.

08
Front

State the three forms of the Law of Cosines.

Back
a2=b2+c2−2bccos⁡A,b2=a2+c2−2accos⁡B,c2=a2+b2−2abcos⁡C.a^2=b^2+c^2-2bc\cos A,\quad b^2=a^2+c^2-2ac\cos B,\quad c^2=a^2+b^2-2ab\cos C.
09
Front

Find the third side for sides 7 and 10 with included angle 60∘60^\circ.

Back

c2=72+102−2(7)(10)cos⁡60∘=79c^2=7^2+10^2-2(7)(10)\cos60^\circ=79, so c=79≈8.9c=\sqrt{79}\approx8.9 units.

10
Front

For sides 88, 1111, and 1313, find the angle opposite side 13.

Back

cos⁡C=82+112−1322(8)(11)=16176\cos C=\frac{8^2+11^2-13^2}{2(8)(11)}=\frac{16}{176}, so C≈84.8∘C\approx84.8^\circ.

11
Front

What is the base-height formula for triangle area?

Back

The base-height formula is K=12bhK=\frac12bh, where hh is perpendicular to the chosen base.

12
Front

Find the area for sides 8 and 11 enclosing a 37∘37^\circ angle.

Back

K=12(8)(11)sin⁡37∘≈26.5K=\frac12(8)(11)\sin37^\circ\approx26.5 square units.