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Oct 26, 2024
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20 changes: 10 additions & 10 deletions source/precalculus/source/06-TR/04.ptx
Original file line number Diff line number Diff line change
Expand Up @@ -100,7 +100,7 @@
</task>
</activity>

<definition xml:id="45-45-90-triangle-rule">
<definition xml:id="def-45-45-90-triangle-rule">
<p>
From <xref ref="exploring-45-45-90-triangle"/>, we saw that a <m>45-45-90</m> triangle is an isosceles right triangle, which means that two of the sides of the triangle are equal. The ratio of its legs and hypotenuse is expressed as follows: <me>\text{Leg}:\text{Leg}:\text{Hypotenuse}=1:1:\sqrt{2}</me>. In terms of <m>x</m>, this ratio can be expressed as <me>x:x:x\sqrt{2}</me>. Therefore, the <term>45-45-90 triangle rule</term> states that the three sides of the triangle are in the ratio <m>x:x:x\sqrt{2}</m>.
</p>
Expand Down Expand Up @@ -129,7 +129,7 @@
<task>
<statement>
<p>
If we apply <xref ref="45-45-90-triangle-rule"/>, what would the length of <m>c</m> be?
If we apply <xref ref="def-45-45-90-triangle-rule"/>, what would the length of <m>c</m> be?
</p>
</statement>
<answer>
Expand All @@ -142,7 +142,7 @@
<task>
<statement>
<p>
If we apply <xref ref="45-45-90-triangle-rule"/>, what would the length of the hypotenuse be?
If we apply <xref ref="def-45-45-90-triangle-rule"/>, what would the length of the hypotenuse be?
</p>
</statement>
<answer>
Expand All @@ -153,10 +153,10 @@
</task>
</activity>

<activity xml:id="45-45-90-practice">
<activity xml:id="activity-45-45-90-practice">
<introduction>
<p>
For each of the following, use <xref ref="45-45-90-triangle-rule"/> to find the missing side.
For each of the following, use <xref ref="def-45-45-90-triangle-rule"/> to find the missing side.
</p>
</introduction>

Expand Down Expand Up @@ -284,7 +284,7 @@
</task>
</activity>

<definition xml:id="30-60-90-triangle-rule">
<definition xml:id="def-30-60-90-triangle-rule">
<p>
From <xref ref="exploring-30-60-90-triangle"/>, we saw that if a triangle has angle measures <m>30</m><degree/>, <m>60</m><degree/>, and <m>90</m><degree/>, then the sides are in the ratio: <me>1:\sqrt{3}:2</me>. In terms of <m>x</m>, this ratio can be expressed as <me>x:x\sqrt{3}:2x</me>. Therefore, the <term>30-60-90 triangle rule</term> states that the three sides of the triangle are in the ratio <m>x:x\sqrt{3}:2x</m>. Note that the shorter leg is always <m>x</m>, the longer leg is always <m>x\sqrt{3}</m>, and the hypotenuse is always <m>2x</m>.
</p>
Expand Down Expand Up @@ -313,7 +313,7 @@
<task>
<statement>
<p>
If we apply <xref ref="30-60-90-triangle-rule"/>, what would the length of <m>a</m> be?
If we apply <xref ref="def-30-60-90-triangle-rule"/>, what would the length of <m>a</m> be?
</p>
</statement>
<answer>
Expand All @@ -326,7 +326,7 @@
<task>
<statement>
<p>
If we apply <xref ref="30-60-90-triangle-rule"/>, what would the length of the hypotenuse be?
If we apply <xref ref="def-30-60-90-triangle-rule"/>, what would the length of the hypotenuse be?
</p>
</statement>
<answer>
Expand All @@ -337,10 +337,10 @@
</task>
</activity>

<activity xml:id="30-60-90-practice">
<activity xml:id="activity-30-60-90-practice">
<introduction>
<p>
For each of the following, use <xref ref="30-60-90-triangle-rule"/> to find the missing side.
For each of the following, use <xref ref="def-30-60-90-triangle-rule"/> to find the missing side.
</p>
</introduction>

Expand Down
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