Solving expressions using 45-45-90 special right triangles

Trigonometry comes from two Greek words that translate to triangle and measure. Trigonometry basically tackles all about measuring a triangle, most especially the right triangles. If you remember our discussion in previous chapter about Pythagorean Theorem, then you would have fully grasped the core of trigonometry.

Pythagorean Theorem is summarized by the equation a2+b2=c2a^2 + b^2 = c^2, where a and b are both sides of the right triangle, and c is the hypotenuse (or the longest side of the right triangle). In the case of Trigonometry, we are to specifically name a side either opposite or adjacent, depending on the angle that is used. Using this knowledge, the six trigonometric functions or ratios are made, which are the sine ratio, tangent ratio, cosine ratio, cotangent ratio, secant ratio, and cosecant ratio we are able to find any missing side, or any missing angle of a right triangle. In using the trigonometric ratios to solve for the measurement of a side, we use angle θ\theta. This is a summary of the six trigonometric functions:

sin θ\theta = opposite/hypotenuse
csc θ\theta = hypotenuse/opposite
cos θ\theta = adjacent/hypotenuse
sec θ\theta = hypotenuse/adjacent
tan θ\theta = opposite/adjacent
cot θ\theta = adjacent/opposite

In this chapter we will also get to learn about the angle of inclination, which is basically the angle formed by the intersection of a line with the x axis. In real life cases, the angle of inclination could mean the angle that you need to see the top of the flagpole. There are plenty of exercises that would entail solving for the angle of inclination. We will also learn about the other angles like angle of elevation and angle of depression in the exercises in this chapter.

By applying these concepts, we will be able to make indirect measurements, like when we want to know the height of a building by just knowing the angle of inclination, and our distance from the building. There are also other word problems found here that would teach us all about indirect measurement.

Solving expressions using 45-45-90 special right triangles


sin45=12 \sin 45^\circ = {1 \over \sqrt 2}
cos45=12 \cos 45^\circ = {1 \over \sqrt 2}
tan45=11=1 \tan 45^\circ = {1 \over 1} = 1

  • 2.
    If θ=45 \theta = 45^\circ , find the exact value of following expressions.
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Solving expressions using 45-45-90 special right triangles

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