What is trigonometry?
2 answers:
Trigonometry is greek for <em>triangle measurement</em>.
Three of the most basic ideas in trigonometry are the <em>sine</em>, <em>cosine</em>, and <em>tangent ratios</em>. The sine, cosine, and tangent ratios can be defined as follows.
I have attached right triangle ABC in the image attached.
In right triangle ABC, the sine of angle A is equal to the ratio of the length of the side opposite angle A to the length of the hypotenuse. So in right triangle ABC, the sine of angle A equals y over z. The abbreviation we use for sine is <u>sin</u>.
Next, the cosine of angle A is equal to the ratio of the length of the side adjacent to angle A to the length of the hypotenuse. So in right triangle ABC, the cosine of angle A equals x over z. The abbreviation we use for cosine is <u>cos</u>.
Finally, the tangent of angle A is equal to the ratio of the length of the side opposite angle A to the length of the side adjacent to angle A. So in right triangle ABC, the tangent of angle A equals y over x. The abbreviation we use for tangent is <u>tan</u>.
An easy way to remember the sine, cosine, and tangent ratios is to use the word SOH-CAH-TOA.
<em>Sine is opposite over hypotenuse, cosine is adjacent over hypotenuse, and tangent is opposite over adjacent.</em>
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The answer is going to be in the picture because trying to make fractions with this is too difficult. :D
The correct pair is option E, which is:
FH ≅ FH - reflexive property
ΔGFH ≅ ΔEFH - SAS theorem
<h3>What is the SAS Congruence Theorem?</h3>The SAS theorems states that two triangles are congruent if they have two pairs of congruent sides and a pair of congruent included angles.
<h3>What is the Reflexive Property?</h3>The reflexive property of geometry states that an angle or line will always be congruent to itself.
In the two column-proof, since FH = FH using the reflexive property, then both triangles are congruent to each other by the SAS congruence theorem.
The missing pair of reasons that completes the proof are:
FH ≅ FH - reflexive property
ΔGFH ≅ ΔEFH - SAS theorem
Learn more about the SAS theorem on:
#SPJ1
